# Definition:Sylow p-Subgroup/Definition 3

## Definition

Let $p$ be prime.

Let $G$ be a finite group whose order is denoted by $\order G$.

Let $n$ be the largest integer such that:

$p^n \divides \order G$

where $\divides$ denotes divisibility.

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

## Source of Name

This entry was named for Peter Ludwig Mejdell Sylow.