# procyclic group

###### Definition.

A group $G$ is a procyclic group if $G$ is a profinite group which is isomorphic^{} to the inverse limit^{} of some projective system of cyclic groups^{}.

###### Example.

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

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

Title | procyclic group |
---|---|

Canonical name | ProcyclicGroup |

Date of creation | 2013-03-22 15:09:14 |

Last modified on | 2013-03-22 15:09:14 |

Owner | alozano (2414) |

Last modified by | alozano (2414) |

Numerical id | 5 |

Author | alozano (2414) |

Entry type | Definition |

Classification | msc 20E18 |

Synonym | pro-cyclic group |

Synonym | pro-cyclic |

Synonym | procyclic |