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    Abelian groups

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    If G is any group, define $:G->G by $(g) = g^-1. Show that G is abelian if an only if $ is a homomorphism.

    © BrainMass Inc. brainmass.com October 9, 2019, 3:51 pm ad1c9bdddf
    https://brainmass.com/math/group-theory/abelian-groups-15169

    Solution Preview

    Proof:
    If G is abelian, then for any x,y in G, we have xy=yx. ...

    Solution Summary

    This is a proof regarding homomorphisms and Abelian groups.

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