Question: G is a finite abelian group of order n. Let d|n.
Prove G has a subgroup of order 'd'.
I know that if p^a (where p is a prime and a any +ve integer) divides n, then G has a subgroup of order p^a
I was trying to use this for the question. Is this correct approach? I have not read the generic theory of abelian groups, so would want to avoid that as much.
Any help/pointers please?