Group theory and generalizations Group actions and permutation groups Concept
Symmetric group
Summary
The symmetric group on a set is the group of all bijections from to , with composition as the operation. For it is written , and its elements are the permutations of symbols.
Where this leads
33 pages build on this one.
- Robinson–Schensted correspondence
- Nichols algebra
- Twelvefold way
- Lagrange's theorem in S3
- Polish group
- Schreier–Sims algorithm
- Representation theory of the symmetric group
- The left cosets of a subgroup of order two in S3
- Jordan's theorem on primitive groups containing a prime cycle
- Robinson–Schensted–Knuth correspondence
- Kaplansky's theorem on PI rings
- Permutation group
- Bruhat order
- Weak order of permutations
- Specht module
- Transformation semigroup
- Little cubes operad
- Posner's theorem
- Algebra over an operad
- Multiply transitive group action
- The cosets of a subgroup that is not normal do not form a group
- Riemann's existence theorem
- Bruhat decomposition of a Lie group
- The symmetric group S3 is not abelian
- Permanent
- Braid group
- The alternating group A3 is normal in S3
- Bruhat decomposition
- The alternating group is the kernel of the sign
- A subgroup of order two in S3 is not normal
- List of small groups
- Orders of the elements of S3
- Amitsur–Levitzki theorem
Further reading
- Web https://en.wikipedia.org/wiki/Symmetric_group, lead section
About this page
| Tag | 0515A6D2Y1 |
|---|---|
| URI | m2://0515A6D2Y1 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20B30 |
| Specializes | Group |
| Same as |
Markdown · JSON · Edit on GitHub
What this page needs for W2
- edge instance_of in: at least two examples (1 of 2)
- 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
Instances
Definitions
Used by
- Robinson–Schensted correspondence
- Twelvefold way
- Lagrange's theorem in S3
- Polish group
- Schreier–Sims algorithm
- Representation theory of the symmetric group
- The left cosets of a subgroup of order two in S3
- Jordan's theorem on primitive groups containing a prime cycle
- Permutation group
- Bruhat order
- Weak order of permutations
- Specht module
- Transformation semigroup
- Little cubes operad
- Algebra over an operad
- Multiply transitive group action
- The cosets of a subgroup that is not normal do not form a group
- Riemann's existence theorem
- The symmetric group S3 is not abelian
- Permanent
- Braid group
- The alternating group A3 is normal in S3
- Bruhat decomposition
- The alternating group is the kernel of the sign
- A subgroup of order two in S3 is not normal
- List of small groups
- Orders of the elements of S3
- Amitsur–Levitzki theorem