Automorphisms And Inner Automorphisms

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Definition (Automorphisms And Inner Automorphisms)

Let $G$ be a group.

• An automorphism of $G$ is an isomorphism from $G$ to $G$.
• We write $\text{Aut}(G)$ to represent the set of all automorphisms of $G$.
• The function $\phi_g:G\to G$ defined by $\phi_g(x)=gxg^{-1}$ is called an inner automorphism of $G$.
• We write $\text{Inn}(G)$ to represent the set of all inner automorphisms of $G$.

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