Let K be a group with 8 elements. Let H be a subgroup of K and H<K. It is known that the size of H is at least 3. The size of H is __________
A. 8
B. 2
C. 3
D. 4
Answer:D
Let K be a group with 8 elements. Let H be a subgroup of K and H<K. It is known that the size of H is at least 3. The size of H is __________
A. 8 B. 2 C. 3 D. 4
Explanation: For any finite group G, the order (number of elements) of every subgroup L of G divides the order of G. G has 8 elements. Factors of 8 are 1, 2, 4 and 8. Since given the size of L is at least 3(1 and 2 eliminated) and not equal to G(8 eliminated), the only size left is 4. Size of L is 4.