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## Homework Statement

Let G be a group of order p

^{2}, where p is a positive prime.

Show that G is isomorphic to either Z/p

^{2}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 p

^{2}then there is a subgroup of order p and of order p

^{2}, which are isomorphic to Zp and Zp

^{2}(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...