1. The problem statement, all variables and given/known data. Let p be a prime number, m a natural number and G a group of order p^m. Prove that there exists an element a in G such that ord(a)=p. 3. The attempt at a solution. I know of the existence of Lagrange theorem, so what I thought was: I pick an arbitrary element a (I exclude e, the identity element) of G and look at the group generated by that element, denoted as <a>. I also know that the order of <a> is equal to the order of the element a. Now I can apply Lagrange theorem: as the order of <a> divides the order of G, then the order of <a> must be of the form p^k for some natural number k, k≤m. I got stuck here, I can't deduce k=1 with only these statements, there is something missing.