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

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

The set of inner automorphisms of $G$ is denoted on as $\Inn G$.

Also denoted as
While $\kappa$ is the symbol generally used on to denote an inner automorphism, this is not universal in the literature.

Different sources use different symbols, for example $\alpha$ as used by.

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

 * Inner Automorphism is Automorphism


 * Inner Automorphisms form Normal Subgroup of Automorphism Group


 * Definition:Inner Automorphism Group