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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- Last edited by Jennifer Paulhus on 2022-07-18 16:03:07
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- columns.gps_groups.outer_group
- columns.gps_groups.outer_order
- group.abstract.336.210.bottom
- lmfdb/groups/abstract/main.py (line 964)
- lmfdb/groups/abstract/main.py (line 1713)
- lmfdb/groups/abstract/main.py (line 1722)
- lmfdb/groups/abstract/stats.py (line 197)
- lmfdb/groups/abstract/templates/abstract-show-group.html (line 25)