# third isomorphism theorem

If $G$ is a group (or ring, or module) and $H$ and $K$ are normal subgroups^{} (or ideals, or submodules^{}, respectively) of $G$, with $H\subseteq K$, then there is a natural isomorphism $(G/H)/(K/H)\cong G/K$.

This is usually known either as the Third Isomorphism Theorem, or as the Second Isomorphism Theorem (depending on the order in which the theorems are introduced). It is also occasionally called the Freshman Theorem.

Title | third isomorphism theorem |
---|---|

Canonical name | ThirdIsomorphismTheorem |

Date of creation | 2013-03-22 12:04:03 |

Last modified on | 2013-03-22 12:04:03 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 12 |

Author | yark (2760) |

Entry type | Theorem |

Classification | msc 20A05 |

Classification | msc 13A15 |

Classification | msc 16D10 |

Synonym | freshman theorem |