# 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:

 $\mathbb{Z}_{p}=\varprojlim\mathbb{Z}/p^{n}\mathbb{Z}.$
Title procyclic group ProcyclicGroup 2013-03-22 15:09:14 2013-03-22 15:09:14 alozano (2414) alozano (2414) 5 alozano (2414) Definition msc 20E18 pro-cyclic group pro-cyclic procyclic