Explore BrainMass

Explore BrainMass

    Some Problems Involving Homomorphisms of Abelian Groups

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    EDIT: G(p) = {x in G : |x| = p^k for some k greater than or equal to 0}

    ** Please see the attachment for the complete problem description **

    © BrainMass Inc. brainmass.com March 4, 2021, 11:30 pm ad1c9bdddf
    https://brainmass.com/math/linear-transformation/problems-involving-homomorphisms-abelian-groups-428527

    Attachments

    Solution Preview

    1. Let g be an element of G(p). Then |g| = p^k for some nonnegative integer k. Now |alpha(g)| must divide |g| = p^k, so we have |alpha(g)| = p^j for some nonnegative integer j <= k. Therefore, alpha(g) must be an element of H(p), so alpha[G(p)] must be a subset of H(p).

    2. First we show that if G and H are isomorphic finite abelian groups and p ...

    Solution Summary

    In this solution, we solve some problems involving homomorphisms an isomorphisms of finite abelian groups.

    $2.49

    ADVERTISEMENT