# subdirect product of groups

Let ${({G}_{i})}_{i\in I}$ be a family of groups.
A subgroup^{} (http://planetmath.org/Subgroup) $H$ of the direct product^{} (http://planetmath.org/DirectProductAndRestrictedDirectProductOfGroups) ${\prod}_{i\in I}{G}_{i}$
is said to be a *subdirect product ^{}* (or

*subcartesian product*) of ${({G}_{i})}_{i\in I}$ if ${\pi}_{i}(H)={G}_{i}$ for each $i\in I$, where ${\pi}_{i}:{\prod}_{i\in I}{G}_{i}\to {G}_{i}$ is the $i$-th projection map.

Title | subdirect product of groups |
---|---|

Canonical name | SubdirectProductOfGroups |

Date of creation | 2013-03-22 14:53:25 |

Last modified on | 2013-03-22 14:53:25 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 7 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 20E26 |

Synonym | subdirect product |

Synonym | subcartesian product |

Synonym | subcartesian product of groups |

Related topic | ResiduallyCalP |

Related topic | DirectProductAndRestrictedDirectProductOfGroups |