# Math Help - Is G abelian?

1. ## Is G abelian?

Let G be a group. H is a subgroup of G. If G/H is abelian and H is abelian, Is G abelian?

I think not.
It is given Hxy = Hyx
This just implies xy(x^-1)(y^-1) is in H
So does this mean H is a commutator subgp?
And is G abelian?

2. Try $G=S_3,\ H=A_3.$