# Sylow’s third theorem

Let $G$ be a finite group^{}, and let $n$ be the number of Sylow
$p$-subgroups^{} of $G$. Then $n\equiv 1\phantom{\rule{veryverythickmathspace}{0ex}}(modp)$, and any
two Sylow $p$-subgroups of $G$ are conjugate to one another.

Title | Sylow’s third theorem |
---|---|

Canonical name | SylowsThirdTheorem |

Date of creation | 2013-03-22 14:00:41 |

Last modified on | 2013-03-22 14:00:41 |

Owner | bwebste (988) |

Last modified by | bwebste (988) |

Numerical id | 19 |

Author | bwebste (988) |

Entry type | Theorem |

Classification | msc 20D20 |

Related topic | SylowTheorems |

Related topic | ProofOfSylowTheorems |

Related topic | SylowPSubgroup |