Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
permutation group |
| gptkbp:actsOn |
set of N elements
|
| gptkbp:centralTo |
trivial group (for N > 2)
|
| gptkbp:conjugacyClasses |
indexed by cycle type
|
| gptkbp:contains |
alternating group A_N
|
| gptkbp:containsElement |
all permutations of N elements
|
| gptkbp:firstNontrivialCase |
gptkb:S_3
|
| gptkbp:generation |
adjacent transpositions
|
| gptkbp:hasSubgroup |
general linear group GL(N, C) (via permutation matrices)
|
| https://www.w3.org/2000/01/rdf-schema#label |
symmetric group S N
|
| gptkbp:identityElement |
identity permutation
|
| gptkbp:isNonAbelian |
false (for N > 2)
|
| gptkbp:isomorphicTo |
automorphism group of N-element set
|
| gptkbp:isSimple |
false (for N > 2, except N=6)
|
| gptkbp:notation |
S_N
|
| gptkbp:order |
N!
|
| gptkbp:outerAutomorphism |
nontrivial only for N=6
|
| gptkbp:presentedBy |
generators: transpositions, relations: Coxeter relations
|
| gptkbp:representationTheory |
irreducible representations correspond to partitions of N
|
| gptkbp:usedIn |
gptkb:algebra
gptkb:algebraic_geometry gptkb:Galois_theory group theory mathematical physics number theory representation theory combinatorics enumerative combinatorics |
| gptkbp:bfsParent |
gptkb:SU(N)
|
| gptkbp:bfsLayer |
6
|