# Normal subgroup

From Diffgeom

*The article on this topic in the Group Properties Wiki can be found at:* normal subgroupTemplate:Subgroup property

## Contents

## Definition

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

- is the kernel of a homomorphism from , i.e. there is a homomorphism of groups such that
- , or in other words, for all