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    Groups : Isomorphism and Homomorphism

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    Show that a group G is simple if and only if every nontrivial group homomorphism G -> G1 is one-to-one.

    © BrainMass Inc. brainmass.com October 9, 2019, 3:53 pm ad1c9bdddf
    https://brainmass.com/math/linear-transformation/groups-isomorphism-and-homomorphism-15977

    Solution Preview

    Proof:
    If G is simple, then G has no nontrivial normal subgroup. Then for any nontrivial group homomorphism f: G->G1, by the isomorphism theory, we have ...

    Solution Summary

    Group simplicity is investigated.

    $2.19