# Definition:Inner Automorphism Group

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## 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**.

## Sources

- Weisstein, Eric W. "Inner Automorphism Group." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/InnerAutomorphismGroup.html