Normal subgroup of order two is central
= Normal subgroup of order two is central
If $N=\{1,z\}$ is a <normal subgroup> of a <group> $G$, conjugation by any element of $G$ preserves $N$ and fixes $1$. It must therefore fix $z$ as well. Thus $N$ lies in the <center of a group>. This fact can turn a small <normal subgroup> into a commuting factor without assuming the whole group is abelian.