If $G$ is a finite group s.t. $|G|=4$, is it abelian ? If $G$ is a finite group s.t. $|G|=4$, is it abelian ? To me it's isomorphic to $\mathbb Z/2\mathbb Z\times \mathbb Z/2\mathbb Z$ or $\mathbb Z/4\mathbb Z$, but a friend of me said that they are not the only group of order 4, and there exist some non-abelian. Do you have such example ?

If $G$ is cyclic, $G$ is abelian. And if $G$ is not cyclic, the order of all elements are equal to $2$. And a group whose all elements are of order $2$ is abelian.
In any cases, a group of order $4$ is abelian.
