Inner automorphism of a group (reviewed)

If $G$ is a group and $g\in G$, then the function $\phi_g:G\to G$ given by conjugation by $g$ \[ \phi_g(x) = gxg^{-1} \] is an automorphism of $G$ called an inner automorphism.

The set of inner automorphisms $\mathrm{Inn}(G)$ is a subgroup of $\Aut(G)$, and \[ \mathrm{Inn}(G) \cong G/Z(G)\] where $Z(G)$ is the center of $G$.