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:

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

Title	pro-$p$ group
Canonical name	PropGroup
Date of creation	2013-03-22 15:09:11
Last modified on	2013-03-22 15:09:11
Owner	alozano (2414)
Last modified by	alozano (2414)
Numerical id	5
Author	alozano (2414)
Entry type	Definition
Classification	msc 20E18
Synonym	pro p group
Synonym	pro-p group
Synonym	pro $p$ group
Related topic	PGroup4