# Definition:Inner Automorphism Group

## Definition

Let $G$ be a group.

The inner automorphism group of $G$ is the algebraic structure:

$\struct {\Inn G, \circ}$

where:

$\Inn G$ is the set of inner automorphisms of $G$
$\circ$ denotes composition of mappings.

## Also denoted as

The inner automorphism group is usually denoted $\Inn G$ when there is little chance of conflating it with the set of inner automorphisms.

## Also see

• Results about inner automorphisms can be found here.