Prove that a finite, simple, Abelian group must be isomorphic to Z_p for some prime p.

I've started a proof, but am getting stuck. I've written..

Let G be a finite, simple, Abelian group. Choose a nonzero element a E G. Consider the set Zg={pg, p E Z}, a nonzero subgroup of G. Since G is finite, it is isomorphic to Zp for some p...

after this, im not sure how to get to the point that p is prime. help please?!