# Jordan-Hölder decomposition

A Jordan–Hölder decomposition of a group $G$ is a filtration^{}

$$G={G}_{1}\supset {G}_{2}\supset \mathrm{\cdots}\supset {G}_{n}=\{1\}$$ |

such that ${G}_{i+1}$ is a normal subgroup^{} of ${G}_{i}$ and the quotient ${G}_{i}/{G}_{i+1}$ is a simple group^{} for each $i$.

Title | Jordan-Hölder decomposition |
---|---|

Canonical name | JordanHolderDecomposition |

Date of creation | 2013-03-22 12:08:41 |

Last modified on | 2013-03-22 12:08:41 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 9 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 20E15 |

Synonym | composition series^{} |

Related topic | DerivedSubgroup |

Related topic | JordanHolderDecompositionTheorem |