Question: Let G be a group and let G = a b a 1 b 1 ; that is, G is the subgroup of all finite

Let G be a group and let G=aba1b1 ; that is, G is the subgroup of all finite

products of elements in G of the form aba1b1 . The subgroup G is called the commutator

subgroup of G.

(a) Show that G is a normal subgroup of G.

(b) Let N be a normal subgroup of G. Prove that G/N is abelian if and only if N contains

the commutator subgroup of G.

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