Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:


Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:


Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:


Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:


Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.
 A. 8
 B. 2
 C. 24
 D. 120
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.
 A. 8
 B. 2
 C. 24
 D. 120
Answer:


Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.
 A. 8
 B. 2
 C. 24
 D. 120
Answer:


Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.
 A. 8
 B. 2
 C. 24
 D. 120
Answer:


Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.
 A. 8
 B. 2
 C. 24
 D. 120
Answer:


Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5
 A. 0
 B. 1
 C. 0,1
 D. 0,4
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5
 A. 0
 B. 1
 C. 0,1
 D. 0,4
Answer:


Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5
 A. 0
 B. 1
 C. 0,1
 D. 0,4
Answer:


Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5
 A. 0
 B. 1
 C. 0,1
 D. 0,4
Answer:


Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5
 A. 0
 B. 1
 C. 0,1
 D. 0,4
Answer:


Question: Statement 1 | A factor group of a non-Abelian group is non-Abelian. Statement 2 | If K is a normal subgroup of H and H is a normal subgroup of G, then K is a normal subgroup of G.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | A factor group of a non-Abelian group is non-Abelian. Statement 2 | If K is a normal subgroup of H and H is a normal subgroup of G, then K is a normal subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | A factor group of a non-Abelian group is non-Abelian. Statement 2 | If K is a normal subgroup of H and H is a normal subgroup of G, then K is a normal subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | A factor group of a non-Abelian group is non-Abelian. Statement 2 | If K is a normal subgroup of H and H is a normal subgroup of G, then K is a normal subgroup of G.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | A factor group of a non-Abelian group is non-Abelian. Statement 2 | If K is a normal subgroup of H and H is a normal subgroup of G, then K is a normal subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | A factor group of a non-Abelian group is non-Abelian. Statement 2 | If K is a normal subgroup of H and H is a normal subgroup of G, then K is a normal subgroup of G.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | A factor group of a non-Abelian group is non-Abelian. Statement 2 | If K is a normal subgroup of H and H is a normal subgroup of G, then K is a normal subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | A factor group of a non-Abelian group is non-Abelian. Statement 2 | If K is a normal subgroup of H and H is a normal subgroup of G, then K is a normal subgroup of G.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | A factor group of a non-Abelian group is non-Abelian. Statement 2 | If K is a normal subgroup of H and H is a normal subgroup of G, then K is a normal subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Find the product of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the product of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].
 A. 2x^2 + 5
 B. 6x^2 + 4x + 6
 C. 0
 D. x^2 + 1
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find the product of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].
 A. 2x^2 + 5
 B. 6x^2 + 4x + 6
 C. 0
 D. x^2 + 1
Answer:


Question: Find the product of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the product of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].
 A. 2x^2 + 5
 B. 6x^2 + 4x + 6
 C. 0
 D. x^2 + 1
Answer:


Question: Find the product of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the product of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].
 A. 2x^2 + 5
 B. 6x^2 + 4x + 6
 C. 0
 D. x^2 + 1
Answer:


Question: Find the product of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the product of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].
 A. 2x^2 + 5
 B. 6x^2 + 4x + 6
 C. 0
 D. x^2 + 1
Answer:


Question: Statement 1 | If a group has an element of order 15 it must have at least 8 elements of order 15. Statement 2 | If a group has more than 8 elements of order 15, it must have at least 16 elements of order 15.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a group has an element of order 15 it must have at least 8 elements of order 15. Statement 2 | If a group has more than 8 elements of order 15, it must have at least 16 elements of order 15.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | If a group has an element of order 15 it must have at least 8 elements of order 15. Statement 2 | If a group has more than 8 elements of order 15, it must have at least 16 elements of order 15.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a group has an element of order 15 it must have at least 8 elements of order 15. Statement 2 | If a group has more than 8 elements of order 15, it must have at least 16 elements of order 15.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a group has an element of order 15 it must have at least 8 elements of order 15. Statement 2 | If a group has more than 8 elements of order 15, it must have at least 16 elements of order 15.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a group has an element of order 15 it must have at least 8 elements of order 15. Statement 2 | If a group has more than 8 elements of order 15, it must have at least 16 elements of order 15.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a group has an element of order 15 it must have at least 8 elements of order 15. Statement 2 | If a group has more than 8 elements of order 15, it must have at least 16 elements of order 15.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a group has an element of order 15 it must have at least 8 elements of order 15. Statement 2 | If a group has more than 8 elements of order 15, it must have at least 16 elements of order 15.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a group has an element of order 15 it must have at least 8 elements of order 15. Statement 2 | If a group has more than 8 elements of order 15, it must have at least 16 elements of order 15.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every homomorphic image of a group G is isomorphic to a factor group of G. Statement 2 | The homomorphic images of a group G are the same (up to isomorphism) as the factor groups of G.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every homomorphic image of a group G is isomorphic to a factor group of G. Statement 2 | The homomorphic images of a group G are the same (up to isomorphism) as the factor groups of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | Every homomorphic image of a group G is isomorphic to a factor group of G. Statement 2 | The homomorphic images of a group G are the same (up to isomorphism) as the factor groups of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every homomorphic image of a group G is isomorphic to a factor group of G. Statement 2 | The homomorphic images of a group G are the same (up to isomorphism) as the factor groups of G.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every homomorphic image of a group G is isomorphic to a factor group of G. Statement 2 | The homomorphic images of a group G are the same (up to isomorphism) as the factor groups of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every homomorphic image of a group G is isomorphic to a factor group of G. Statement 2 | The homomorphic images of a group G are the same (up to isomorphism) as the factor groups of G.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every homomorphic image of a group G is isomorphic to a factor group of G. Statement 2 | The homomorphic images of a group G are the same (up to isomorphism) as the factor groups of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every homomorphic image of a group G is isomorphic to a factor group of G. Statement 2 | The homomorphic images of a group G are the same (up to isomorphism) as the factor groups of G.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every homomorphic image of a group G is isomorphic to a factor group of G. Statement 2 | The homomorphic images of a group G are the same (up to isomorphism) as the factor groups of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | A ring homomorphism is one to one if and only if the kernel is {0}. Statement 2 | Q is an ideal in R.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | A ring homomorphism is one to one if and only if the kernel is {0}. Statement 2 | Q is an ideal in R.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | A ring homomorphism is one to one if and only if the kernel is {0}. Statement 2 | Q is an ideal in R.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | A ring homomorphism is one to one if and only if the kernel is {0}. Statement 2 | Q is an ideal in R.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | A ring homomorphism is one to one if and only if the kernel is {0}. Statement 2 | Q is an ideal in R.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | A ring homomorphism is one to one if and only if the kernel is {0}. Statement 2 | Q is an ideal in R.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | A ring homomorphism is one to one if and only if the kernel is {0}. Statement 2 | Q is an ideal in R.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | A ring homomorphism is one to one if and only if the kernel is {0}. Statement 2 | Q is an ideal in R.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | A ring homomorphism is one to one if and only if the kernel is {0}. Statement 2 | Q is an ideal in R.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Find the degree for the given field extension Q(sqrt(2) + sqrt(3)) over Q.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the degree for the given field extension Q(sqrt(2) + sqrt(3)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find the degree for the given field extension Q(sqrt(2) + sqrt(3)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:


Question: Find the degree for the given field extension Q(sqrt(2) + sqrt(3)) over Q.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the degree for the given field extension Q(sqrt(2) + sqrt(3)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:


Question: Find the degree for the given field extension Q(sqrt(2) + sqrt(3)) over Q.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the degree for the given field extension Q(sqrt(2) + sqrt(3)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:


Question: Find the degree for the given field extension Q(sqrt(2) + sqrt(3)) over Q.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the degree for the given field extension Q(sqrt(2) + sqrt(3)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:


Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7
 A. 1
 B. 2
 C. 2,3
 D. 6
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7
 A. 1
 B. 2
 C. 2,3
 D. 6
Answer:


Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7
 A. 1
 B. 2
 C. 2,3
 D. 6
Answer:


Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7
 A. 1
 B. 2
 C. 2,3
 D. 6
Answer:


Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7
 A. 1
 B. 2
 C. 2,3
 D. 6
Answer:


Question: Statement 1 | If H is a subgroup of G and a belongs to G then |aH| = |Ha|. Statement 2 | If H is a subgroup of G and a and b belong to G, then aH and Hb are identical or disjoint.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H is a subgroup of G and a belongs to G then |aH| = |Ha|. Statement 2 | If H is a subgroup of G and a and b belong to G, then aH and Hb are identical or disjoint.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | If H is a subgroup of G and a belongs to G then |aH| = |Ha|. Statement 2 | If H is a subgroup of G and a and b belong to G, then aH and Hb are identical or disjoint.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H is a subgroup of G and a belongs to G then |aH| = |Ha|. Statement 2 | If H is a subgroup of G and a and b belong to G, then aH and Hb are identical or disjoint.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H is a subgroup of G and a belongs to G then |aH| = |Ha|. Statement 2 | If H is a subgroup of G and a and b belong to G, then aH and Hb are identical or disjoint.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H is a subgroup of G and a belongs to G then |aH| = |Ha|. Statement 2 | If H is a subgroup of G and a and b belong to G, then aH and Hb are identical or disjoint.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H is a subgroup of G and a belongs to G then |aH| = |Ha|. Statement 2 | If H is a subgroup of G and a and b belong to G, then aH and Hb are identical or disjoint.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H is a subgroup of G and a belongs to G then |aH| = |Ha|. Statement 2 | If H is a subgroup of G and a and b belong to G, then aH and Hb are identical or disjoint.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H is a subgroup of G and a belongs to G then |aH| = |Ha|. Statement 2 | If H is a subgroup of G and a and b belong to G, then aH and Hb are identical or disjoint.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is
 A. symmetric only
 B. anti-symmetric only
 C. both symmetric and anti-symmetric
 D. an equivalence relation
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is
 A. symmetric only
 B. anti-symmetric only
 C. both symmetric and anti-symmetric
 D. an equivalence relation
Answer:


Question: If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is
 A. symmetric only
 B. anti-symmetric only
 C. both symmetric and anti-symmetric
 D. an equivalence relation
Answer:


Question: If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is
 A. symmetric only
 B. anti-symmetric only
 C. both symmetric and anti-symmetric
 D. an equivalence relation
Answer:


Question: If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is
 A. symmetric only
 B. anti-symmetric only
 C. both symmetric and anti-symmetric
 D. an equivalence relation
Answer:


Question: Find the order of the factor group (Z_11 x Z_15)/(<1, 1>)

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the order of the factor group (Z_11 x Z_15)/(<1, 1>)
 A. 1
 B. 2
 C. 5
 D. 11
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find the order of the factor group (Z_11 x Z_15)/(<1, 1>)
 A. 1
 B. 2
 C. 5
 D. 11
Answer:


Question: Find the order of the factor group (Z_11 x Z_15)/(<1, 1>)

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the order of the factor group (Z_11 x Z_15)/(<1, 1>)
 A. 1
 B. 2
 C. 5
 D. 11
Answer:


Question: Find the order of the factor group (Z_11 x Z_15)/(<1, 1>)

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the order of the factor group (Z_11 x Z_15)/(<1, 1>)
 A. 1
 B. 2
 C. 5
 D. 11
Answer:


Question: Find the order of the factor group (Z_11 x Z_15)/(<1, 1>)

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the order of the factor group (Z_11 x Z_15)/(<1, 1>)
 A. 1
 B. 2
 C. 5
 D. 11
Answer:


Question: The polynomial x^3 + 2x^2 + 2x + 1 can be factored into linear factors in Z_7[x]. Find this factorization.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The polynomial x^3 + 2x^2 + 2x + 1 can be factored into linear factors in Z_7[x]. Find this factorization.
 A. (x − 2)(x + 2)(x − 1)
 B. (x + 1)(x + 4)(x − 2)
 C. (x + 1)(x − 4)(x − 2)
 D. (x - 1)(x − 4)(x − 2)
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: The polynomial x^3 + 2x^2 + 2x + 1 can be factored into linear factors in Z_7[x]. Find this factorization.
 A. (x − 2)(x + 2)(x − 1)
 B. (x + 1)(x + 4)(x − 2)
 C. (x + 1)(x − 4)(x − 2)
 D. (x - 1)(x − 4)(x − 2)
Answer:


Question: The polynomial x^3 + 2x^2 + 2x + 1 can be factored into linear factors in Z_7[x]. Find this factorization.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The polynomial x^3 + 2x^2 + 2x + 1 can be factored into linear factors in Z_7[x]. Find this factorization.
 A. (x − 2)(x + 2)(x − 1)
 B. (x + 1)(x + 4)(x − 2)
 C. (x + 1)(x − 4)(x − 2)
 D. (x - 1)(x − 4)(x − 2)
Answer:


Question: The polynomial x^3 + 2x^2 + 2x + 1 can be factored into linear factors in Z_7[x]. Find this factorization.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The polynomial x^3 + 2x^2 + 2x + 1 can be factored into linear factors in Z_7[x]. Find this factorization.
 A. (x − 2)(x + 2)(x − 1)
 B. (x + 1)(x + 4)(x − 2)
 C. (x + 1)(x − 4)(x − 2)
 D. (x - 1)(x − 4)(x − 2)
Answer:


Question: The polynomial x^3 + 2x^2 + 2x + 1 can be factored into linear factors in Z_7[x]. Find this factorization.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The polynomial x^3 + 2x^2 + 2x + 1 can be factored into linear factors in Z_7[x]. Find this factorization.
 A. (x − 2)(x + 2)(x − 1)
 B. (x + 1)(x + 4)(x − 2)
 C. (x + 1)(x − 4)(x − 2)
 D. (x - 1)(x − 4)(x − 2)
Answer:


Question: Find the maximum possible order for an element of S_n for n = 10.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the maximum possible order for an element of S_n for n = 10.
 A. 6
 B. 12
 C. 30
 D. 105
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find the maximum possible order for an element of S_n for n = 10.
 A. 6
 B. 12
 C. 30
 D. 105
Answer:


Question: Find the maximum possible order for an element of S_n for n = 10.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the maximum possible order for an element of S_n for n = 10.
 A. 6
 B. 12
 C. 30
 D. 105
Answer:


Question: Find the maximum possible order for an element of S_n for n = 10.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the maximum possible order for an element of S_n for n = 10.
 A. 6
 B. 12
 C. 30
 D. 105
Answer:


Question: Find the maximum possible order for an element of S_n for n = 10.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the maximum possible order for an element of S_n for n = 10.
 A. 6
 B. 12
 C. 30
 D. 105
Answer:


Question: Statement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: The inverse of -i in the multiplicative group, {1, -1, i , -i} is

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The inverse of -i in the multiplicative group, {1, -1, i , -i} is
 A. 1
 B. -1
 C. i
 D. -i
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: The inverse of -i in the multiplicative group, {1, -1, i , -i} is
 A. 1
 B. -1
 C. i
 D. -i
Answer:


Question: The inverse of -i in the multiplicative group, {1, -1, i , -i} is

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The inverse of -i in the multiplicative group, {1, -1, i , -i} is
 A. 1
 B. -1
 C. i
 D. -i
Answer:


Question: The inverse of -i in the multiplicative group, {1, -1, i , -i} is

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The inverse of -i in the multiplicative group, {1, -1, i , -i} is
 A. 1
 B. -1
 C. i
 D. -i
Answer:


Question: The inverse of -i in the multiplicative group, {1, -1, i , -i} is

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The inverse of -i in the multiplicative group, {1, -1, i , -i} is
 A. 1
 B. -1
 C. i
 D. -i
Answer:


Question: Compute the product in the given ring. (2,3)(3,5) in Z_5 x Z_9

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Compute the product in the given ring. (2,3)(3,5) in Z_5 x Z_9
 A. (1,1)
 B. (3,1)
 C. (1,6)
 D. (3,6)
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Compute the product in the given ring. (2,3)(3,5) in Z_5 x Z_9
 A. (1,1)
 B. (3,1)
 C. (1,6)
 D. (3,6)
Answer:


Question: Compute the product in the given ring. (2,3)(3,5) in Z_5 x Z_9

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Compute the product in the given ring. (2,3)(3,5) in Z_5 x Z_9
 A. (1,1)
 B. (3,1)
 C. (1,6)
 D. (3,6)
Answer:


Question: Compute the product in the given ring. (2,3)(3,5) in Z_5 x Z_9

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Compute the product in the given ring. (2,3)(3,5) in Z_5 x Z_9
 A. (1,1)
 B. (3,1)
 C. (1,6)
 D. (3,6)
Answer:


Question: Compute the product in the given ring. (2,3)(3,5) in Z_5 x Z_9

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Compute the product in the given ring. (2,3)(3,5) in Z_5 x Z_9
 A. (1,1)
 B. (3,1)
 C. (1,6)
 D. (3,6)
Answer:


Question: The set of all real numbers under the usual multiplication operation is not a group since

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The set of all real numbers under the usual multiplication operation is not a group since
 A. multiplication is not a binary operation
 B. multiplication is not associative
 C. identity element does not exist
 D. zero has no inverse
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: The set of all real numbers under the usual multiplication operation is not a group since
 A. multiplication is not a binary operation
 B. multiplication is not associative
 C. identity element does not exist
 D. zero has no inverse
Answer:


Question: The set of all real numbers under the usual multiplication operation is not a group since

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The set of all real numbers under the usual multiplication operation is not a group since
 A. multiplication is not a binary operation
 B. multiplication is not associative
 C. identity element does not exist
 D. zero has no inverse
Answer:


Question: The set of all real numbers under the usual multiplication operation is not a group since

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The set of all real numbers under the usual multiplication operation is not a group since
 A. multiplication is not a binary operation
 B. multiplication is not associative
 C. identity element does not exist
 D. zero has no inverse
Answer:


Question: The set of all real numbers under the usual multiplication operation is not a group since

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The set of all real numbers under the usual multiplication operation is not a group since
 A. multiplication is not a binary operation
 B. multiplication is not associative
 C. identity element does not exist
 D. zero has no inverse
Answer:


Question: Statement 1| Every group of order p^2 where p is prime is Abelian. Statement 2 | For a fixed prime p a Sylow p-subgroup of a group G is a normal subgroup of G if and only if it is the only Sylow p-subgroup of G.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1| Every group of order p^2 where p is prime is Abelian. Statement 2 | For a fixed prime p a Sylow p-subgroup of a group G is a normal subgroup of G if and only if it is the only Sylow p-subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1| Every group of order p^2 where p is prime is Abelian. Statement 2 | For a fixed prime p a Sylow p-subgroup of a group G is a normal subgroup of G if and only if it is the only Sylow p-subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1| Every group of order p^2 where p is prime is Abelian. Statement 2 | For a fixed prime p a Sylow p-subgroup of a group G is a normal subgroup of G if and only if it is the only Sylow p-subgroup of G.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1| Every group of order p^2 where p is prime is Abelian. Statement 2 | For a fixed prime p a Sylow p-subgroup of a group G is a normal subgroup of G if and only if it is the only Sylow p-subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1| Every group of order p^2 where p is prime is Abelian. Statement 2 | For a fixed prime p a Sylow p-subgroup of a group G is a normal subgroup of G if and only if it is the only Sylow p-subgroup of G.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1| Every group of order p^2 where p is prime is Abelian. Statement 2 | For a fixed prime p a Sylow p-subgroup of a group G is a normal subgroup of G if and only if it is the only Sylow p-subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1| Every group of order p^2 where p is prime is Abelian. Statement 2 | For a fixed prime p a Sylow p-subgroup of a group G is a normal subgroup of G if and only if it is the only Sylow p-subgroup of G.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1| Every group of order p^2 where p is prime is Abelian. Statement 2 | For a fixed prime p a Sylow p-subgroup of a group G is a normal subgroup of G if and only if it is the only Sylow p-subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | For finite groups G and H, |G + H| = |G||H|. (G + H is the internal direct product.) Statement 2 | If r divides m and s divides n then Z_m + Z_n has a subgroup isomorphic to Z_r + Z_s.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | For finite groups G and H, |G + H| = |G||H|. (G + H is the internal direct product.) Statement 2 | If r divides m and s divides n then Z_m + Z_n has a subgroup isomorphic to Z_r + Z_s.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | For finite groups G and H, |G + H| = |G||H|. (G + H is the internal direct product.) Statement 2 | If r divides m and s divides n then Z_m + Z_n has a subgroup isomorphic to Z_r + Z_s.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | For finite groups G and H, |G + H| = |G||H|. (G + H is the internal direct product.) Statement 2 | If r divides m and s divides n then Z_m + Z_n has a subgroup isomorphic to Z_r + Z_s.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | For finite groups G and H, |G + H| = |G||H|. (G + H is the internal direct product.) Statement 2 | If r divides m and s divides n then Z_m + Z_n has a subgroup isomorphic to Z_r + Z_s.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | For finite groups G and H, |G + H| = |G||H|. (G + H is the internal direct product.) Statement 2 | If r divides m and s divides n then Z_m + Z_n has a subgroup isomorphic to Z_r + Z_s.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | For finite groups G and H, |G + H| = |G||H|. (G + H is the internal direct product.) Statement 2 | If r divides m and s divides n then Z_m + Z_n has a subgroup isomorphic to Z_r + Z_s.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | For finite groups G and H, |G + H| = |G||H|. (G + H is the internal direct product.) Statement 2 | If r divides m and s divides n then Z_m + Z_n has a subgroup isomorphic to Z_r + Z_s.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | For finite groups G and H, |G + H| = |G||H|. (G + H is the internal direct product.) Statement 2 | If r divides m and s divides n then Z_m + Z_n has a subgroup isomorphic to Z_r + Z_s.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Find the sum of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the sum of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].
 A. 2x^2 + 5
 B. 6x^2 + 4x + 6
 C. 0
 D. x^2 + 1
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find the sum of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].
 A. 2x^2 + 5
 B. 6x^2 + 4x + 6
 C. 0
 D. x^2 + 1
Answer:


Question: Find the sum of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the sum of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].
 A. 2x^2 + 5
 B. 6x^2 + 4x + 6
 C. 0
 D. x^2 + 1
Answer:


Question: Find the sum of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the sum of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].
 A. 2x^2 + 5
 B. 6x^2 + 4x + 6
 C. 0
 D. x^2 + 1
Answer:


Question: Find the sum of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the sum of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].
 A. 2x^2 + 5
 B. 6x^2 + 4x + 6
 C. 0
 D. x^2 + 1
Answer:


Question: Statement 1 | Any set of two vectors in R^2 is linearly independent. Statement 2 | If V = span(v1, ... , vk) and {v1, ... , vk} are linearly independent, then dim(V) = k.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Any set of two vectors in R^2 is linearly independent. Statement 2 | If V = span(v1, ... , vk) and {v1, ... , vk} are linearly independent, then dim(V) = k.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | Any set of two vectors in R^2 is linearly independent. Statement 2 | If V = span(v1, ... , vk) and {v1, ... , vk} are linearly independent, then dim(V) = k.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Any set of two vectors in R^2 is linearly independent. Statement 2 | If V = span(v1, ... , vk) and {v1, ... , vk} are linearly independent, then dim(V) = k.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Any set of two vectors in R^2 is linearly independent. Statement 2 | If V = span(v1, ... , vk) and {v1, ... , vk} are linearly independent, then dim(V) = k.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Any set of two vectors in R^2 is linearly independent. Statement 2 | If V = span(v1, ... , vk) and {v1, ... , vk} are linearly independent, then dim(V) = k.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Any set of two vectors in R^2 is linearly independent. Statement 2 | If V = span(v1, ... , vk) and {v1, ... , vk} are linearly independent, then dim(V) = k.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Any set of two vectors in R^2 is linearly independent. Statement 2 | If V = span(v1, ... , vk) and {v1, ... , vk} are linearly independent, then dim(V) = k.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Any set of two vectors in R^2 is linearly independent. Statement 2 | If V = span(v1, ... , vk) and {v1, ... , vk} are linearly independent, then dim(V) = k.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: The set of all nth roots of unity under multiplication of complex numbers form a/an

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The set of all nth roots of unity under multiplication of complex numbers form a/an
 A. semi group with identity
 B. commutative semigroups with identity
 C. group
 D. abelian group
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: The set of all nth roots of unity under multiplication of complex numbers form a/an
 A. semi group with identity
 B. commutative semigroups with identity
 C. group
 D. abelian group
Answer:


Question: The set of all nth roots of unity under multiplication of complex numbers form a/an

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The set of all nth roots of unity under multiplication of complex numbers form a/an
 A. semi group with identity
 B. commutative semigroups with identity
 C. group
 D. abelian group
Answer:


Question: The set of all nth roots of unity under multiplication of complex numbers form a/an

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The set of all nth roots of unity under multiplication of complex numbers form a/an
 A. semi group with identity
 B. commutative semigroups with identity
 C. group
 D. abelian group
Answer:


Question: The set of all nth roots of unity under multiplication of complex numbers form a/an

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The set of all nth roots of unity under multiplication of complex numbers form a/an
 A. semi group with identity
 B. commutative semigroups with identity
 C. group
 D. abelian group
Answer:


Question: Statement 1 | Every maximal ideal is a prime ideal. Statement 2 | If I is a maximal ideal of a commutative ring R, then R/I is field.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every maximal ideal is a prime ideal. Statement 2 | If I is a maximal ideal of a commutative ring R, then R/I is field.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | Every maximal ideal is a prime ideal. Statement 2 | If I is a maximal ideal of a commutative ring R, then R/I is field.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every maximal ideal is a prime ideal. Statement 2 | If I is a maximal ideal of a commutative ring R, then R/I is field.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every maximal ideal is a prime ideal. Statement 2 | If I is a maximal ideal of a commutative ring R, then R/I is field.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every maximal ideal is a prime ideal. Statement 2 | If I is a maximal ideal of a commutative ring R, then R/I is field.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every maximal ideal is a prime ideal. Statement 2 | If I is a maximal ideal of a commutative ring R, then R/I is field.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every maximal ideal is a prime ideal. Statement 2 | If I is a maximal ideal of a commutative ring R, then R/I is field.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every maximal ideal is a prime ideal. Statement 2 | If I is a maximal ideal of a commutative ring R, then R/I is field.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an
 A. subgroup
 B. finite abelian group
 C. infinite, non abelian group
 D. ininite, abelian
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an
 A. subgroup
 B. finite abelian group
 C. infinite, non abelian group
 D. ininite, abelian
Answer:


Question: Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an
 A. subgroup
 B. finite abelian group
 C. infinite, non abelian group
 D. ininite, abelian
Answer:


Question: Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an
 A. subgroup
 B. finite abelian group
 C. infinite, non abelian group
 D. ininite, abelian
Answer:


Question: Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an
 A. subgroup
 B. finite abelian group
 C. infinite, non abelian group
 D. ininite, abelian
Answer:


Question: Statement 1 | Every group of order 42 has a normal subgroup of order 7. Statement 2 | Every group of order 42 has a normal subgroup of order 8.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every group of order 42 has a normal subgroup of order 7. Statement 2 | Every group of order 42 has a normal subgroup of order 8.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | Every group of order 42 has a normal subgroup of order 7. Statement 2 | Every group of order 42 has a normal subgroup of order 8.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every group of order 42 has a normal subgroup of order 7. Statement 2 | Every group of order 42 has a normal subgroup of order 8.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every group of order 42 has a normal subgroup of order 7. Statement 2 | Every group of order 42 has a normal subgroup of order 8.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every group of order 42 has a normal subgroup of order 7. Statement 2 | Every group of order 42 has a normal subgroup of order 8.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every group of order 42 has a normal subgroup of order 7. Statement 2 | Every group of order 42 has a normal subgroup of order 8.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every group of order 42 has a normal subgroup of order 7. Statement 2 | Every group of order 42 has a normal subgroup of order 8.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every group of order 42 has a normal subgroup of order 7. Statement 2 | Every group of order 42 has a normal subgroup of order 8.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Determine whether the polynomial in Z[x] satisfies an Eisenstein criterion for irreducibility over Q. 8x^3 + 6x^2 - 9x + 24

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Determine whether the polynomial in Z[x] satisfies an Eisenstein criterion for irreducibility over Q. 8x^3 + 6x^2 - 9x + 24
 A. Yes, with p=2.
 B. Yes, with p=3.
 C. Yes, with p=5.
 D. No.
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Determine whether the polynomial in Z[x] satisfies an Eisenstein criterion for irreducibility over Q. 8x^3 + 6x^2 - 9x + 24
 A. Yes, with p=2.
 B. Yes, with p=3.
 C. Yes, with p=5.
 D. No.
Answer:


Question: Determine whether the polynomial in Z[x] satisfies an Eisenstein criterion for irreducibility over Q. 8x^3 + 6x^2 - 9x + 24

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Determine whether the polynomial in Z[x] satisfies an Eisenstein criterion for irreducibility over Q. 8x^3 + 6x^2 - 9x + 24
 A. Yes, with p=2.
 B. Yes, with p=3.
 C. Yes, with p=5.
 D. No.
Answer:


Question: Determine whether the polynomial in Z[x] satisfies an Eisenstein criterion for irreducibility over Q. 8x^3 + 6x^2 - 9x + 24

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Determine whether the polynomial in Z[x] satisfies an Eisenstein criterion for irreducibility over Q. 8x^3 + 6x^2 - 9x + 24
 A. Yes, with p=2.
 B. Yes, with p=3.
 C. Yes, with p=5.
 D. No.
Answer:


Question: Determine whether the polynomial in Z[x] satisfies an Eisenstein criterion for irreducibility over Q. 8x^3 + 6x^2 - 9x + 24

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Determine whether the polynomial in Z[x] satisfies an Eisenstein criterion for irreducibility over Q. 8x^3 + 6x^2 - 9x + 24
 A. Yes, with p=2.
 B. Yes, with p=3.
 C. Yes, with p=5.
 D. No.
Answer:


Question: Statement 1 | The image of a group of 6 elements under a homomorphism may have 12 elements. Statement 2 | There is a homomorphism of some group of 6 elements into some group of 12 elements.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | The image of a group of 6 elements under a homomorphism may have 12 elements. Statement 2 | There is a homomorphism of some group of 6 elements into some group of 12 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | The image of a group of 6 elements under a homomorphism may have 12 elements. Statement 2 | There is a homomorphism of some group of 6 elements into some group of 12 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | The image of a group of 6 elements under a homomorphism may have 12 elements. Statement 2 | There is a homomorphism of some group of 6 elements into some group of 12 elements.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | The image of a group of 6 elements under a homomorphism may have 12 elements. Statement 2 | There is a homomorphism of some group of 6 elements into some group of 12 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | The image of a group of 6 elements under a homomorphism may have 12 elements. Statement 2 | There is a homomorphism of some group of 6 elements into some group of 12 elements.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | The image of a group of 6 elements under a homomorphism may have 12 elements. Statement 2 | There is a homomorphism of some group of 6 elements into some group of 12 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | The image of a group of 6 elements under a homomorphism may have 12 elements. Statement 2 | There is a homomorphism of some group of 6 elements into some group of 12 elements.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | The image of a group of 6 elements under a homomorphism may have 12 elements. Statement 2 | There is a homomorphism of some group of 6 elements into some group of 12 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | The homomorphic image of a cyclic group is cyclic. Statement 2 | The homomorphic image of an Abelian group is Abelian.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | The homomorphic image of a cyclic group is cyclic. Statement 2 | The homomorphic image of an Abelian group is Abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | The homomorphic image of a cyclic group is cyclic. Statement 2 | The homomorphic image of an Abelian group is Abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | The homomorphic image of a cyclic group is cyclic. Statement 2 | The homomorphic image of an Abelian group is Abelian.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | The homomorphic image of a cyclic group is cyclic. Statement 2 | The homomorphic image of an Abelian group is Abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | The homomorphic image of a cyclic group is cyclic. Statement 2 | The homomorphic image of an Abelian group is Abelian.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | The homomorphic image of a cyclic group is cyclic. Statement 2 | The homomorphic image of an Abelian group is Abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | The homomorphic image of a cyclic group is cyclic. Statement 2 | The homomorphic image of an Abelian group is Abelian.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | The homomorphic image of a cyclic group is cyclic. Statement 2 | The homomorphic image of an Abelian group is Abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H is a subgroup of a group G and a belongs to G, then aH = Ha. Statement 2 | If H is normal of G and a belongs to G, then ah = ha for all h in H.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H is a subgroup of a group G and a belongs to G, then aH = Ha. Statement 2 | If H is normal of G and a belongs to G, then ah = ha for all h in H.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | If H is a subgroup of a group G and a belongs to G, then aH = Ha. Statement 2 | If H is normal of G and a belongs to G, then ah = ha for all h in H.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H is a subgroup of a group G and a belongs to G, then aH = Ha. Statement 2 | If H is normal of G and a belongs to G, then ah = ha for all h in H.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H is a subgroup of a group G and a belongs to G, then aH = Ha. Statement 2 | If H is normal of G and a belongs to G, then ah = ha for all h in H.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H is a subgroup of a group G and a belongs to G, then aH = Ha. Statement 2 | If H is normal of G and a belongs to G, then ah = ha for all h in H.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H is a subgroup of a group G and a belongs to G, then aH = Ha. Statement 2 | If H is normal of G and a belongs to G, then ah = ha for all h in H.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H is a subgroup of a group G and a belongs to G, then aH = Ha. Statement 2 | If H is normal of G and a belongs to G, then ah = ha for all h in H.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H is a subgroup of a group G and a belongs to G, then aH = Ha. Statement 2 | If H is normal of G and a belongs to G, then ah = ha for all h in H.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: If (G, .) is a group such that (ab)^-1 = a^-1b^-1, for all a, b in G, then G is a/an

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: If (G, .) is a group such that (ab)^-1 = a^-1b^-1, for all a, b in G, then G is a/an
 A. commutative semi group
 B. abelian group
 C. non-abelian group
 D. None of these
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: If (G, .) is a group such that (ab)^-1 = a^-1b^-1, for all a, b in G, then G is a/an
 A. commutative semi group
 B. abelian group
 C. non-abelian group
 D. None of these
Answer:


Question: If (G, .) is a group such that (ab)^-1 = a^-1b^-1, for all a, b in G, then G is a/an

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: If (G, .) is a group such that (ab)^-1 = a^-1b^-1, for all a, b in G, then G is a/an
 A. commutative semi group
 B. abelian group
 C. non-abelian group
 D. None of these
Answer:


Question: If (G, .) is a group such that (ab)^-1 = a^-1b^-1, for all a, b in G, then G is a/an

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: If (G, .) is a group such that (ab)^-1 = a^-1b^-1, for all a, b in G, then G is a/an
 A. commutative semi group
 B. abelian group
 C. non-abelian group
 D. None of these
Answer:


Question: If (G, .) is a group such that (ab)^-1 = a^-1b^-1, for all a, b in G, then G is a/an

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: If (G, .) is a group such that (ab)^-1 = a^-1b^-1, for all a, b in G, then G is a/an
 A. commutative semi group
 B. abelian group
 C. non-abelian group
 D. None of these
Answer:


Question: Statement 1 | In a finite dimensional vector space every linearly independent set of vectors is contained in a basis. Statement 2 | If B_1 and B_2 are bases for the same vector space, then |B_1| = |B_2|.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | In a finite dimensional vector space every linearly independent set of vectors is contained in a basis. Statement 2 | If B_1 and B_2 are bases for the same vector space, then |B_1| = |B_2|.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | In a finite dimensional vector space every linearly independent set of vectors is contained in a basis. Statement 2 | If B_1 and B_2 are bases for the same vector space, then |B_1| = |B_2|.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | In a finite dimensional vector space every linearly independent set of vectors is contained in a basis. Statement 2 | If B_1 and B_2 are bases for the same vector space, then |B_1| = |B_2|.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | In a finite dimensional vector space every linearly independent set of vectors is contained in a basis. Statement 2 | If B_1 and B_2 are bases for the same vector space, then |B_1| = |B_2|.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | In a finite dimensional vector space every linearly independent set of vectors is contained in a basis. Statement 2 | If B_1 and B_2 are bases for the same vector space, then |B_1| = |B_2|.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | In a finite dimensional vector space every linearly independent set of vectors is contained in a basis. Statement 2 | If B_1 and B_2 are bases for the same vector space, then |B_1| = |B_2|.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | In a finite dimensional vector space every linearly independent set of vectors is contained in a basis. Statement 2 | If B_1 and B_2 are bases for the same vector space, then |B_1| = |B_2|.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | In a finite dimensional vector space every linearly independent set of vectors is contained in a basis. Statement 2 | If B_1 and B_2 are bases for the same vector space, then |B_1| = |B_2|.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G?

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G?
 A. g = g^-1 for every g in G
 B. g = g^2 for every g in G
 C. (g o h)^2 = g^2 o h^2 for every g,h in G
 D. G is of finite order
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G?
 A. g = g^-1 for every g in G
 B. g = g^2 for every g in G
 C. (g o h)^2 = g^2 o h^2 for every g,h in G
 D. G is of finite order
Answer:


Question: Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G?

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G?
 A. g = g^-1 for every g in G
 B. g = g^2 for every g in G
 C. (g o h)^2 = g^2 o h^2 for every g,h in G
 D. G is of finite order
Answer:


Question: Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G?

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G?
 A. g = g^-1 for every g in G
 B. g = g^2 for every g in G
 C. (g o h)^2 = g^2 o h^2 for every g,h in G
 D. G is of finite order
Answer:


Question: Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G?

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G?
 A. g = g^-1 for every g in G
 B. g = g^2 for every g in G
 C. (g o h)^2 = g^2 o h^2 for every g,h in G
 D. G is of finite order
Answer:


Question: Statement 1 | If T: V -> W is a linear transformation and dim(V ) < dim(W) < 1, then T must be injective. Statement 2 | Let dim(V) = n and suppose that T: V -> V is linear. If T is injective, then it is a bijection.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If T: V -> W is a linear transformation and dim(V ) < dim(W) < 1, then T must be injective. Statement 2 | Let dim(V) = n and suppose that T: V -> V is linear. If T is injective, then it is a bijection.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | If T: V -> W is a linear transformation and dim(V ) < dim(W) < 1, then T must be injective. Statement 2 | Let dim(V) = n and suppose that T: V -> V is linear. If T is injective, then it is a bijection.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If T: V -> W is a linear transformation and dim(V ) < dim(W) < 1, then T must be injective. Statement 2 | Let dim(V) = n and suppose that T: V -> V is linear. If T is injective, then it is a bijection.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If T: V -> W is a linear transformation and dim(V ) < dim(W) < 1, then T must be injective. Statement 2 | Let dim(V) = n and suppose that T: V -> V is linear. If T is injective, then it is a bijection.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If T: V -> W is a linear transformation and dim(V ) < dim(W) < 1, then T must be injective. Statement 2 | Let dim(V) = n and suppose that T: V -> V is linear. If T is injective, then it is a bijection.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If T: V -> W is a linear transformation and dim(V ) < dim(W) < 1, then T must be injective. Statement 2 | Let dim(V) = n and suppose that T: V -> V is linear. If T is injective, then it is a bijection.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If T: V -> W is a linear transformation and dim(V ) < dim(W) < 1, then T must be injective. Statement 2 | Let dim(V) = n and suppose that T: V -> V is linear. If T is injective, then it is a bijection.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If T: V -> W is a linear transformation and dim(V ) < dim(W) < 1, then T must be injective. Statement 2 | Let dim(V) = n and suppose that T: V -> V is linear. If T is injective, then it is a bijection.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3)) over Q.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:


Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3)) over Q.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:


Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3)) over Q.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer:


Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3)) over Q.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3)) over Q.
 A. 0
 B. 4
 C. 2
 D. 6
Answer: