# locally $\mathcal{P}$

Let $\mathcal{P}$ be a property of groups.
A group $G$ is said to be *locally $\mathrm{P}$* if every nontrivial finitely generated subgroup of $G$ has property $\mathcal{P}$.

For example, the locally infinite groups are precisely the torsion-free groups. Other classes of groups defined this way include locally finite groups and locally cyclic groups.

Title | locally $\mathcal{P}$ |
---|---|

Canonical name | LocallycalP |

Date of creation | 2013-03-22 14:18:57 |

Last modified on | 2013-03-22 14:18:57 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 5 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 20E25 |

Related topic | GeneralizedCyclicGroup |

Related topic | LocallyFiniteGroup |

Related topic | LocallyNilpotentGroup |