1. The problem statement, all variables and given/known data An abelian group has order pn (where p is a prime) and contains p-1 elements of order p. Prove that this group is cyclic. 2. Relevant equations 3. 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.