I'm trying to dust off the cobb webs by studying some basic Group Theory. Can someone provide a proof that a Group of order 5, or any prime for that matter, must be a cyclic Abelian group, and that there can be only one such group...

I can easily find the multiplication table for the Group, but I don't see how to prove the statement that it is the only such group.

Any insights would be much appreciated..

Thanks