Group theory/Inner automorphism/Definition

Let ${\displaystyle {}G}$ be a group, and ${\displaystyle {}g\in G}$ be fixed. The mapping defined by ${\displaystyle {}g}$,

${\displaystyle \kappa _{g}\colon G\longrightarrow G,x\longmapsto gxg^{-1},}$

is called an inner automorphism.