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:

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