Definition:Sylow p-Subgroup/Definition 2
Let $p$ be prime.
Let $G$ be a finite group.
A Sylow $p$-subgroup of $G$ is a maximal $p$-subgroup $P$ of $G$.
In this context, maximality means that if $Q$ is a $p$-subgroup of $G$ and $P \le Q$, then $P = Q$.
Source of Name
This entry was named for Peter Ludwig Mejdell Sylow.