A normal subgroup is ____________
A. a subgroup under multiplication by the elements of the group
B. an invariant under closure by the elements of that group
C. a monoid with same number of elements of the original group
D. an invariant equipped with conjugation by the elements of original group
Answer:D
A normal subgroup is ____________
A. a subgroup under multiplication by the elements of the group B. an invariant under closure by the elements of that group C. a monoid with same number of elements of the original group D. an invariant equipped with conjugation by the elements of original group
Explanation: A normal subgroup is a subgroup that is invariant under conjugation by any element of the original group that is, K is normal if and only if gKg-1=K for any g belongs to G Equivalently, a subgroup K of G is normal if and only if gK=Kg for any g belongs to G.Normal subgroups are useful in constructing quotient groups and in analyzing homomorphisms.