# Schreier refinement theorem

The *Schreier Refinement Theorem* states that any two subnormal series for a group have equivalent^{} refinements^{}.
Here, two subnormal series are considered equivalent if they have the same factors (up to isomorphism^{}), not necessarily in the same order.

This theorem can be used to prove the Jordan-HÃ¶lder Theorem (http://planetmath.org/JordanHolderDecompositionTheorem), and can also be used to prove that the Hirsch number of a polycyclic group is well-defined.

Title | Schreier refinement theorem |
---|---|

Canonical name | SchreierRefinementTheorem |

Date of creation | 2013-03-22 14:40:53 |

Last modified on | 2013-03-22 14:40:53 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 8 |

Author | yark (2760) |

Entry type | Theorem |

Classification | msc 20E15 |