1. The problem statement, all variables and given/known data How would I prove that gnhn = (gh)n, for g,h [itex]\in[/itex]G where G is a p-group, and all its elements have order p? 3. The attempt at a solution My aim is to prove this in order to prove that G is Abelian, but I don't want to prove it using centres. I've supposed that gnhn = (gh)m for some m, and now I'm trying to prove that m must be congruent to n modulo p, as this is the only way that (gh)m = (gh)n since gh has order p. And this is where I strike a wall, so to speak. Is there a better way to prove that G is Abelian, if this isn't good enough? Thanks!!