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
Canonical name	SylowsFirstTheorem
Date of creation	2013-03-22 14:00:46
Last modified on	2013-03-22 14:00:46
Owner	bwebste (988)
Last modified by	bwebste (988)
Numerical id	11
Author	bwebste (988)
Entry type	Theorem
Classification	msc 20D20
Related topic	SylowTheorems
Related topic	ProofOfSylowTheorems