# Central factor of normal subgroup

From Groupprops

This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: central factor and normal subgroup

View other such compositions|View all subgroup properties

## Contents

## Definition

### Symbol-free definition

A subgroup of a group is termed a **central factor of normal subgroup** if it satisfies the following equivalent conditions:

- It is a central factor of a normal subgroup of the whole group.
- It is a central factor inside its normal closure.

## Relation with other properties

### Stronger properties

- Normal subgroup
- Base of a wreath product
- Direct factor of normal subgroup
- Direct factor of characteristic subgroup
- Subgroup of Abelian normal subgroup