Let G be a group of order p2, where p is a positive prime.
Show that G is isomorphic to either Z/p2 or Z/p × Z/p.
The Attempt at a Solution
Am I completely wrong here or is this just the definition of a p-Sylow subgroup? what I mean is that if g is of order p2 then there is a subgroup of order p and of order p2, which are isomorphic to Zp and Zp2 (respectively).
Also, if the Sylow group is isomorphic to Zp, it is abelian, would that consequently make G abelian? Not too sure how to put all this into mathematical form...