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If $G$ is a group, its inner automorphism group is a normal subgroup of the full automorphism group. Then, the outer automorphism group of $G$ is \[ \mathrm{Out}(G) = \Aut(G)/\mathrm{Inn}(G).\]

Note that the term outer automorphism is often used to mean any automorphism of a group $G$ which is not an inner automorphism. In this case, the nontrivial elements of the outer automorphism group are cosets of outer automorphisms.

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  • Review status: reviewed
  • Last edited by Jennifer Paulhus on 2022-07-18 16:03:07
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