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 $G$.

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- Review status: reviewed
- Last edited by Jennifer Paulhus on 2022-07-18 16:00:05

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