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Math Help - Is G abelian?

  1. #1
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    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?
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  2. #2
    Junior Member
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    Try G=S_3,\ H=A_3.
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