# Finite CN-group

From Groupprops

This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: finite group and CN-group

View other group property conjunctions OR view all group properties

## Definition

A **finite CN-group** is a finite group that is also a CN-group.

## Facts

### Basic facts

- Sylow subgroups for distinct primes in CN-group centralize each other iff they have non-identity elements that centralize each other
- Commuting of non-identity elements defines an equivalence relation between prime divisors of the order of a finite CN-group