Definition:Sylow p-Subgroup/Definition 3

Definition
Let $p$ be prime.

Let $G$ be a finite group whose order is denoted by $\left\vert{G}\right\vert$. Let $n$ be the largest integer such that:
 * $p^n \mathrel \backslash \left\vert{G}\right\vert$

where $\backslash$ denotes divisibility.

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

Also see

 * Equivalence of Definitions of Sylow $p$-Subgroup