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

How would I prove that g^{n}h^{n}= (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 g^{n}h^{n}= (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!!

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# Homework Help: Abelian p-group

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