# normal is not transitive

The phrase “normal is not transitive” can be used as a mnemonic for two statements.

The first is: “The relation^{} ‘is a normal subgroup^{} of’ is not transitive^{}.” This means that, if $H\u25c1N\u25c1G$, it does not follow that $H\u25c1G$. See normality of subgroups is not transitive for more details.

The second is: “The relation ‘is a normal extension^{} of’ is not transitive.” This means that, if $K/F$ and $L/K$ are normal extensions, it does not follow that $L/F$ is normal. See example of normal extension for more details.

Title | normal is not transitive |
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Canonical name | NormalIsNotTransitive |

Date of creation | 2013-03-22 16:00:34 |

Last modified on | 2013-03-22 16:00:34 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 9 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 20A05 |

Classification | msc 12F10 |

Related topic | ExampleOfNormalExtension |

Related topic | NormalityOfSubgroupsIsNotTransitive |