State Lagrange's Theorem. Deduce that if $G$ is a finite group of order $n$, then the order of every element of $G$ is a divisor of $n$.

Let $G$ be a group such that, for every $g \in G, g^{2}=e$. Show that $G$ is abelian. Give an example of a non-abelian group in which every element $g$ satisfies $g^{4}=e$.