Prove that if a finite abelian group has order a power of a prime p, then the order of every element in the group is a power of p. Can the hypothesis...

Prove that if a finite abelian group has order a power of a prime p, then the order of every element in the group is a power of p. Can the hypothesis of commutativity be dropped? Why or why not?Let G be an abelian group of order 72. Can you see how many subgroups of order 8 G has? Why or why not?