#
nLab

quotient group

### Context

#### Group Theory

**group theory**

### Classical groups

### Finite groups

### Group schemes

### Topological groups

### Lie groups

### Super-Lie groups

### Higher groups

### Cohomology and Extensions

# Contents

## Idea

A *quotient group* is a quotient object in the category Grp of groups.

## Definition

For $G$ a group and $H \hookrightarrow G$ a normal subgroup, the quotient group $G/H$ is the set of cosets, equipped with a group structure induced from $G$.

## Examples

- For $A \hookrightarrow B$ a morphism between abelian groups the quotient $B/A$ is equivalently the cokernel of the inclusion.

Revised on September 12, 2012 03:37:52
by

Toby Bartels
(98.19.47.153)