Definition:Inner Automorphism

Definition
Let $G$ be a group.

Let $x \in G$.

Let the mapping $\kappa_x: G \to G$ be defined such that $\forall g \in G: \kappa_x \left({g}\right) = x g x^{-1}$.

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

The set of all inner automorphisms of $G$ is denoted $\operatorname{Inn} \left({G}\right)$ or $\mathscr I \left({G}\right)$.

Also see

 * Inner Automorphism is an Automorphism