Inner Automorphism Group

A particular type of Automorphism Group which exists only for Groups. For a Group $G$, the inner automorphism group is defined by

$$\mathop{\rm Inn}\nolimits (G)=\{\sigma_a: a\in G\}\subset \mathop{\rm Aut}\nolimits (G)$$

where $\sigma_a$ is an Automorphism of $G$ defined by

$$\sigma_a(x)=axa^{-1}.$$

See also Automorphism, Automorphism Group