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but is it the case that for all factors of the order of a group there is an element of that order?? i am soo confused..

Hi I have a problem I just can't seem to solve, even though the solution shouldn't be too hard Let G be a finite abelian group and let p be a prime. Suppose that any non-trivial element g in G has order p. Show that the order of G must be p^n for some positive integer n. Anyone got any...