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## Homework Statement

Let G be a finite p-group, where p is a positive prime. Show that G has nontrivial center. In other words Z(G) [itex]\neq[/itex] {e}.

## The Attempt at a Solution

So the centre is pretty much the "abelian subgroup" of G, or all the elements that commute with every other element. Now I remember that if G has prime order, then it is abelian, but I can't find the proof, although I'm not sure if that was a "if and only if" statement or if it was one sided... So if I can prove that, then Z(G) is just equal to G?