I need to prove the following:
Let G be a group.
If s.t. , then (S is the commutator subgroup).
I just need a lead here...
Thank you in advance.
I think the commutator subgroup of G is universally denoted by G'. The easiest way to answer your question is to work in the factor group G/G'. However a direct approach is:
Let h be in H and g in G. Then [g,h-1]=g-1hgh-1 is in H and so g-1hg is in H.