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    Groups : Isomorphism and Homomorphism

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    S4 means symmetric group of degree 4
    A4 means alternating group of degree 4
    e is the identity

    Is there a group homomorphism $:S4 -> A4, with
    kernel $ = {e, (1 2)(3 4), (1 3)(2 4), (1 4)(2 3)}?

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    Solution Preview

    By the isomorphism theory, if there is a group homomorphism $: S4->A4, ...

    Solution Summary

    A group homomorphism is investigated.