# 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 $N\lhd G$ such that $S\cap N=\{1\}$ and $SN=G$.

Title Burnside normal complement theorem BurnsideNormalComplementTheorem 2013-03-22 13:16:22 2013-03-22 13:16:22 bwebste (988) bwebste (988) 5 bwebste (988) Theorem msc 20D20