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?

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- Dec 12th 2009, 03:49 AMpoornaIs 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? - Dec 12th 2009, 03:57 AMproscientia
Try $\displaystyle G=S_3,\ H=A_3.$