A finite group is nilpotent if and only if its Sylow subgroups are normal

A finite group is nilpotent exactly when every Sylow subgroup is normal.Suggest a slogan

Let $G$ be a finite group. Then $G$ is nilpotent if and only if, for every prime $p$ dividing $\abs{G}$, the Sylow $p$-subgroup of $G$ is normal.