(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

3. 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...

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# Group of p-power order isomorphism

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