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
