Burnside normal complement theorem

Let $G$ be a finite group, and $S$ a Sylow subgroup such that $C_G(S)=N_G(S)$. Then $S$ has a normal complement. That is, there exists a normal subgroup $N⊲G$ such that $S\cap N=\{1\}$ and $SN=G$.

Title	Burnside normal complement theorem
Canonical name	BurnsideNormalComplementTheorem
Date of creation	2013-03-22 13:16:22
Last modified on	2013-03-22 13:16:22
Owner	bwebste (988)
Last modified by	bwebste (988)
Numerical id	5
Author	bwebste (988)
Entry type	Theorem
Classification	msc 20D20