Definition:Inner Automorphism

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Definition

Let $G$ be a group.

Let $x \in G$.

Let the mapping $\kappa_x: G \to G$ be defined such that:

$\forall g \in G: \map {\kappa_x} g = x g x^{-1}$


$\kappa_x$ is called the inner automorphism of $G$ (given) by $x$.


The set of inner automorphisms of $G$ is denoted on $\mathsf{Pr} \infty \mathsf{fWiki}$ as $\Inn G$.


Also denoted as

The set of inner automorphisms of $G$ can be found denoted in a number of ways, for example:

$\map {\mathscr I} G$
$\map I G$


Also see

  • Results about inner automorphisms can be found here.


Sources