# Some Problems Involving Homomorphisms of Abelian Groups

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

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 **

Â© BrainMass Inc. brainmass.com March 4, 2021, 11:30 pm ad1c9bdddfhttps://brainmass.com/math/linear-transformation/problems-involving-homomorphisms-abelian-groups-428527

#### 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