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If $G$ is a group and $g\in G$, then the function $\phi_g:G\to G$ given by $\phi_g(x) = gxg^{-1}$ 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: beta
• Last edited by John Jones on 2019-05-23 19:14:50
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