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## Homework Statement

An abelian group has order p

^{n}(where p is a prime) and contains p-1 elements of order p. Prove that this group is cyclic.

## Homework Equations

## The Attempt at a Solution

I know I should use the theorem for classifying finite abelian groups, which I understand, and I feel like I have all the pieces but I don't know how to put them together.