Hello, community! I've been struggling forever with this problem. Let G be abelian and G(n) denote the set of elements g of G such that g^n=e. I'm asked to prove G(n) is a subgroup which is okay, nothing really special about it. However, I'm also asked to prove that given any prime p, it is true that |G(p)|^2 ≥ |G(p^2)|, where the bars help denote the number of elements in each group. Thanks for any help!

Pd: G is also finite.