Let $G$ be a group and let $g\in G$. Define a homomorphism $\varphi_g: G\to G$ by $\varphi_g(x) = gxg^{-1}$ for all $x\in G$. These $\varphi_g$ are in fact automorphisms and moreover $\varphi_g\circ\varphi_h = \varphi_{gh}$. The $\varphi_g$ are called inner automorphisms of $G$.
Wikidata ID: Q1139583