Definition:Sylow p-Subgroup/Definition 1

Definition
Let $p$ be prime.

Let $G$ be a finite group. Let the order of $G$ be given by $\left|{G}\right| = k p^n$ where $p \nmid k$.

A Sylow $p$-subgroup is a $p$-subgroup of $G$ which has $p^n$ elements.