Group theory and generalizations Group actions and permutation groups Concept
Group action
Summary
An action of a group on a set lets each element of move the points of . The moves must respect the group operation. Equivalently, it is a group homomorphism from to the symmetric group of .
Where this leads
34 pages build on this one.
- Equivariant cohomology
- Kuranishi structure
- Topological dynamics
- Group cohomology
- Block system
- Proper group action
- Algebraic combinatorics
- Wreath product
- Principal bundle
- Group action on a variety
- Skew group ring
- Permutation group
- Category of elements
- Primitive permutation group
- Moment map
- Bredon cohomology
- Torsor
- CAT(0) group
- Quasi-invariant measure
- Lie group action
- Amenable group action
- Algebra over an operad
- Multiply transitive group action
- Topological transformation group
- Pólya enumeration theorem
- Erlangen program
- Švarc–Milnor lemma
- Crossed product
- Ring of invariants
- Properly discontinuous action
- Fundamental domain
- Associated bundle
- Frobenius group
- Functor category
Further reading
- Web https://en.wikipedia.org/wiki/Group_action, lead section
About this page
| Tag | 0WCY42EV9V |
|---|---|
| URI | m2://0WCY42EV9V |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20B05 |
| Same as |
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What this page needs for W2
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Special cases
- Transitive action
- Faithful action
- Topological transformation group
- Lie group action
- Proper group action
- Group action on a variety
Instances
Definitions
Used by
- Equivariant cohomology
- Kuranishi structure
- Topological dynamics
- Group cohomology
- Block system
- Proper group action
- Algebraic combinatorics
- Wreath product
- Principal bundle
- Group action on a variety
- Skew group ring
- Permutation group
- Category of elements
- Primitive permutation group
- Moment map
- Bredon cohomology
- Torsor
- CAT(0) group
- Quasi-invariant measure
- Lie group action
- Amenable group action
- Algebra over an operad
- Multiply transitive group action
- Topological transformation group
- Pólya enumeration theorem
- Erlangen program
- Švarc–Milnor lemma
- Crossed product
- Ring of invariants
- Properly discontinuous action
- Fundamental domain
- Associated bundle
- Frobenius group
- Functor category