# divisible closure

Let $G$ be a torsion-free abelian group. We will say that $D$ is the divisible closure of $G$ if $D$ is the only divisible torsion-free group between $G$ and $D$, or equivalently, if for each $x\in D$ there exists a non-negative integer $n$ such that $nx\in G$.

Title | divisible closure |
---|---|

Canonical name | DivisibleClosure |

Date of creation | 2013-03-22 15:58:36 |

Last modified on | 2013-03-22 15:58:36 |

Owner | polarbear (3475) |

Last modified by | polarbear (3475) |

Numerical id | 5 |

Author | polarbear (3475) |

Entry type | Definition |

Classification | msc 20K35 |

Defines | divisible closure of a group |