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