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gptkbp:instanceOf
|
gptkb:group_of_people
permutation group
|
|
gptkbp:actsOn
|
set of n elements
|
|
gptkbp:application
|
gptkb:topology
gptkb:Galois_theory
chemistry
physics
representation theory
combinatorics
|
|
gptkbp:automorphismGroup
|
order 2 (for n = 6)
trivial (for n ≠ 6)
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gptkbp:centralTo
|
trivial group (for n > 2)
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gptkbp:conjugacyClasses
|
indexed by partitions of n
|
|
gptkbp:containsElement
|
all permutations of n elements
|
|
gptkbp:generation
|
adjacent transpositions
|
|
gptkbp:hasNormalSubgroup
|
gptkb:alternating_group_A_n_(for_n_>_2)
|
|
gptkbp:hasSubgroup
|
gptkb:alternating_group_A_n
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
symmetric group S n
|
|
gptkbp:identityElement
|
identity 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
|
permutations (symmetry)
|
|
gptkbp:notation
|
gptkb:S_n
|
|
gptkbp:operator
|
composition of permutations
|
|
gptkbp:order
|
n!
|
|
gptkbp:presentedBy
|
Coxeter presentation
|
|
gptkbp:bfsParent
|
gptkb:Weyl_group
|
|
gptkbp:bfsLayer
|
5
|