# 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^{} $N\u22b2G$ 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 |