# 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.

Title Sylow’s first theorem SylowsFirstTheorem 2013-03-22 14:00:46 2013-03-22 14:00:46 bwebste (988) bwebste (988) 11 bwebste (988) Theorem msc 20D20 SylowTheorems ProofOfSylowTheorems