# 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 |