Contents

group theory

# 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.

• The quotient groups of any group by itself is the trivial group: $G/G = 1$.

Last revised on May 26, 2022 at 09:36:04. See the history of this page for a list of all contributions to it.