# 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:

 $\mathbb{Z}_{p}=\varprojlim\mathbb{Z}/p^{n}\mathbb{Z}.$
Title pro-$p$ group PropGroup 2013-03-22 15:09:11 2013-03-22 15:09:11 alozano (2414) alozano (2414) 5 alozano (2414) Definition msc 20E18 pro p group pro-p group pro $p$ group PGroup4