# supersolvable group

A group $G$ is *supersolvable* if it has a finite normal series^{}

$$G={G}_{0}\u22b3{G}_{1}\u22b3\mathrm{\cdots}\u22b3{G}_{n}=1$$ |

with the property that each factor group ${G}_{i-1}/{G}_{i}$ is cyclic.

A supersolvable group is solvable.

Finitely generated^{} nilpotent groups^{} are supersolvable.

Title | supersolvable group |
---|---|

Canonical name | SupersolvableGroup |

Date of creation | 2013-03-22 13:58:44 |

Last modified on | 2013-03-22 13:58:44 |

Owner | mclase (549) |

Last modified by | mclase (549) |

Numerical id | 5 |

Author | mclase (549) |

Entry type | Definition |

Classification | msc 20F16 |

Classification | msc 20D10 |

Related topic | PolycyclicGroup |

Defines | supersolvable |