# Homework Help: Algbra Proof

1. Nov 3, 2008

### Unassuming

1. The problem statement, all variables and given/known data

A finite,commutative grp is not cyclic

iff

it has a subgrp that is isomorphic to (Z mod p) x (Z mod p) , for a prime p.

2. Relevant equations

I am having trouble and I would appreciate a hint.

3. The attempt at a solution

Let G be a finite commutative grp with order n.

Assume that G is not cyclic. This means that there are no elements in G which are relatively prime with n and n is not a prime otherwise it would be cyclic.

Last edited: Nov 3, 2008
2. Nov 3, 2008

### morphism

This doesn't make sense. Instead, you want to notice that n must have a repeated prime factor. The fact that G is commutative is vital here.

3. Nov 5, 2008

### Unassuming

Could you give me an example of this? I am having trouble without an example and I had the misconception that "comm. iff cyclic". I now see the theorem in the book and it's only one way.

There is also a note in the book that, A subgrp of a comm. grp has the same left and right cosets.

4. Nov 5, 2008

### morphism

Example of what? A commutative noncyclic group? (Z mod p) x (Z mod p) is one!