Group theory and generalizations Foundations Concept
Automorphism group
Summary
The automorphism group of a group is the group of all isomorphisms from to itself, with composition as the operation. It describes the symmetries of the structure of .
Where this leads
13 pages build on this one.
- Ryll-Nardzewski theorem
- Poincaré's theorem that the ball and polydisc are not biholomorphic
- Conway groups
- Hurwitz's automorphisms theorem
- Holomorphic automorphisms of C^n
- Out(F_n)
- Fraïssé limit
- Multiply transitive group action
- Characterizations of Galois extensions
- Mathieu groups
- Artin's theorem on fixed fields
- O'Nan–Scott theorem
- Chevalley group
Further reading
- Web https://en.wikipedia.org/wiki/Automorphism_group, lead section
About this page
| Tag | 0K1SCPBNKJ |
|---|---|
| URI | m2://0K1SCPBNKJ |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20F28 |
| Specializes | Group |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Definitions
Used by
- Ryll-Nardzewski theorem
- Poincaré's theorem that the ball and polydisc are not biholomorphic
- Conway groups
- Hurwitz's automorphisms theorem
- Holomorphic automorphisms of C^n
- Out(F_n)
- Fraïssé limit
- Characterizations of Galois extensions
- Mathieu groups
- Artin's theorem on fixed fields
- O'Nan–Scott theorem
- Chevalley group