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:

$${\mathbb{Z}}_p=\underleftarrow{\lim }\mathbb{Z}/p^n\mathbb{Z}.$$

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