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

Let p be a prime and let H be a group of order p^n, some n > 0. Prove that for any x not equal to 1 in H, some power of x has order p.

2. Relevant equations

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3. The attempt at a solution

I know that by lagrange, for any x in G, if x is not the identity, then x has an order p^r for some r>0. Also I know that there is some element of order p. But I don't know how to show that some power of every p^r = p, even though it seems almost intuitive.

Thanks very much!

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# Homework Help: P-groups and orders of elements

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