# Abelian groups

Let G be group of order 54

a. If G is abelian, what groups can it be up to isomorphisms

b. If G is nonabelian and the order of G is 24 and G is isomorphic to H x Z_3, what are the possibilities for H up to isomorphism

c. If p and q are distinct primes, how many abelian groups are there of order p (square) q(fourth)?

https://brainmass.com/math/group-theory/abelian-group-problems-384970

#### Solution Summary

This solution demonstrates how to solve the given problems regarding abelian groups.

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