|
gptkbp:instanceOf
|
gptkb:group_of_people
permutation group
|
|
gptkbp:actsOn
|
finite set
|
|
gptkbp:centralTo
|
trivial (for n>2)
|
|
gptkbp:conjugacyClasses
|
indexed by cycle type
|
|
gptkbp:contains
|
gptkb:group_of_people
|
|
gptkbp:containsElement
|
permutation
|
|
gptkbp:field
|
abstract algebra
|
|
gptkbp:generation
|
adjacent transpositions
|
|
gptkbp:hasSubgroup
|
gptkb:group_of_people
dihedral group
itself
cyclic group
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Symmetric group
|
|
gptkbp:identityElement
|
identity permutation
inverse permutation
|
|
gptkbp:isNonAbelian
|
false (for n>2)
true (for n=1,2)
|
|
gptkbp:isomorphicTo
|
automorphism group of n-element set
|
|
gptkbp:isSimple
|
false (for n>4)
true (for n=5)
|
|
gptkbp:namedAfter
|
gptkb:symmetry
|
|
gptkbp:notation
|
gptkb:S_n
|
|
gptkbp:operator
|
composition of permutations
|
|
gptkbp:order
|
n!
|
|
gptkbp:relatedTo
|
gptkb:Sylow_theorems
gptkb:group_of_people
gptkb:Jordan–Hölder_theorem
gptkb:Young_tableau
gptkb:Burnside's_lemma
gptkb:Cayley's_theorem
gptkb:Schur-Weyl_duality
gptkb:Young_subgroup
representation ring
permutation matrix
character table
cycle decomposition
simple group
solvable group
wreath product
group action
transpositions
|
|
gptkbp:representationTheory
|
well-studied
|
|
gptkbp:studiedBy
|
gptkb:Évariste_Galois
gptkb:Augustin-Louis_Cauchy
|
|
gptkbp:usedIn
|
gptkb:topology
gptkb:Galois_theory
mathematical physics
representation theory
combinatorics
|
|
gptkbp:bfsParent
|
gptkb:Triangle_Group
|
|
gptkbp:bfsLayer
|
5
|