Inner Automorphisms with Groups
Let $G$ be a group, and let $g \in G$ . Prove that the function $\gamma_g: G \to G$ defined by $(\forall a \epsilon g): \gamma_g(a)=g a^{-1} g $ is an automorphism of G.
The automorphisms $\gamma_g$ are called 'inner' automorphisms.
Hints:
If $b\in G$, notice that $b=gg^{-1}bgg^{-1}$.
If $gag^{-1}=1$, solve for $a$.