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gptkbp:instanceOf
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gptkb:group_of_people
permutation group
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gptkbp:actsOn
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set of n+1 elements
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gptkbp:automorphismGroup
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gptkb:complete_graph_K_{n+1}
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gptkbp:centralTo
|
trivial group (for n+1 > 2)
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gptkbp:contains
|
gptkb:alternating_group_A_{n+1}
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|
gptkbp:hasSubgroup
|
gptkb:alternating_group_A_{n+1}
gptkb:dihedral_group_of_order_2(n+1)
cyclic group of order n+1
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|
https://www.w3.org/2000/01/rdf-schema#label
|
symmetric group S {n+1}
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|
gptkbp:isCayleyGroup
|
true
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|
gptkbp:isGeneratedBy
|
adjacent transpositions
|
|
gptkbp:isNonAbelian
|
true (for n+1 > 2)
|
|
gptkbp:isPrimitive
|
true
|
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gptkbp:isSimple
|
false (for n+1 > 4)
|
|
gptkbp:isSolvable
|
true (for n+1 < 5), false (for n+1 >= 5)
|
|
gptkbp:isTransitiveOn
|
true
|
|
gptkbp:isUniversal
|
every finite group is a subgroup of some S_n
|
|
gptkbp:isWeylGroupOf
|
type A_n
|
|
gptkbp:order
|
(n+1)!
|
|
gptkbp:presentedBy
|
generators s_i, relations s_i^2=1, (s_i s_{i+1})^3=1, (s_i s_j)^2=1 for |i-j|>1
|
|
gptkbp:relatedTo
|
gptkb:Galois_theory
gptkb:Young_tableaux
representation theory
combinatorics
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|
gptkbp:represents
|
permutation matrices
|
|
gptkbp:bfsParent
|
gptkb:(n+1)-dimensional_Hamming_cube
gptkb:A_n_root_system
gptkb:Weyl_group_of_type_A_n
gptkb:simple_Lie_algebra_of_type_A_n
|
|
gptkbp:bfsLayer
|
7
|