# pro-$p$ group

###### Definition.

Let $p$ be a prime number. A group $G$ is a pro-$p$ group if $G$ is a profinite group which is isomorphic^{} to the inverse limit^{} of some projective system of $p$-groups (http://planetmath.org/PGroup4).

###### Example.

The $p$-adic integers (http://planetmath.org/PAdicIntegers) ${\mathbb{Z}}_{p}$ form a pro-$p$ group since:

$${\mathbb{Z}}_{p}=\underleftarrow{\mathrm{lim}}\mathbb{Z}/{p}^{n}\mathbb{Z}.$$ |

Title | pro-$p$ group |
---|---|

Canonical name | PropGroup |

Date of creation | 2013-03-22 15:09:11 |

Last modified on | 2013-03-22 15:09:11 |

Owner | alozano (2414) |

Last modified by | alozano (2414) |

Numerical id | 5 |

Author | alozano (2414) |

Entry type | Definition |

Classification | msc 20E18 |

Synonym | pro p group |

Synonym | pro-p group |

Synonym | pro $p$ group |

Related topic | PGroup4 |