Definition:Sylow p-Subgroup/Definition 2

Definition

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.