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    Group homomorphism

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    Problem 3:
    Define µ : Z4 × Z6 -> Z4 × Z3 by
    µ ([x]4,[y]6) = ([x+2y]4,[y]3).
    (a) Show that µ is a well-defined group homomorphism.
    (b) Find the kernel and image of µ, and apply the fundamental homomorphism theorem.

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    Solution Preview

    Please see attached file.
    Problem 3:


    (a) If y1 y2 (mod 6), then 2y1 - 2y2 is divisible by 12, so

    2y1 2y2 (mod 4), and then it ...

    Solution Summary

    This is a proof regarding a well-defined group homomorphism, and shows how to find kernel and image.