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:

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