Normalizer of a subgroup (reviewed)

If $H$ is a subgroup of a group $G$, then the normalizer of $H$ is the subgroup \[ N_G(H) = \{ g\in G\mid gHg^{-1} = H\}.\] Equivalently, $N_G(H)$ is the largest subgroup of $G$ containing $H$ in which $H$ is normal.