A Group of Order the Square of a Prime is Abelian
Problem 20
Suppose the order of a group $G$ is $p^2$, where $p$ is a prime number.
Show that
(a) the group $G$ is an abelian group, and
(b) the group $G$ is isomorphic to either $\Zmod{p^2}$ or $\Zmod{p} \times \Zmod{p}$ without using the fundamental theorem of abelian groups.
Add to solve later 
