# proper subgroup

A *proper subgroup ^{}* of a group $G$
is a subgroup

^{}$H$ of $G$ such that $H\ne G$.

The only subgroup of $G$ that is not a proper subgroup is $G$ itself,
which may therefore occasionally be called an *improper subgroup*.

Title | proper subgroup |
---|---|

Canonical name | ProperSubgroup |

Date of creation | 2013-03-22 12:49:10 |

Last modified on | 2013-03-22 12:49:10 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 7 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 20A99 |

Related topic | Subgroup |

Related topic | Group |

Defines | improper subgroup |