Sylow’s first theorem

If $G$ is a finite group and $p$ is a prime (http://planetmath.org/Prime) such that $p^k$ divides $|G|$, then there is a subgroup (http://planetmath.org/Subgroup) $H$ of $G$ such that $|H|=p^k$.

This is the first part of several results usually called the Sylow theorems.