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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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Z/2Z for n-1 = 6
trivial for n-1 ≠ 6
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gptkbp:CayleyTable
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permutations of n-1 elements
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gptkbp:centralTo
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trivial for n-1 > 2
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gptkbp:conjugacyClasses
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indexed by cycle type
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gptkbp:contains
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gptkb:alternating_group_A_{n-1}
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gptkbp:generation
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(1 2), (1 2 ... n-1)
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gptkbp:hasNormalSubgroup
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gptkb:alternating_group_A_{n-1}
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gptkbp:hasSubgroup
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gptkb:symmetric_group_S_n
gptkb:alternating_group_A_{n-1}
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https://www.w3.org/2000/01/rdf-schema#label
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symmetric group S {n-1}
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gptkbp:isNonAbelian
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for n-1 > 2
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gptkbp:isomorphicTo
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automorphism group of set with n-1 elements
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gptkbp:isSimple
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false for n-1 > 2
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gptkbp:isSolvable
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false for n-1 >= 5
true for n-1 < 5
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gptkbp:isTransitiveOn
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true
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gptkbp:minimalDegree
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n-1
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gptkbp:notation
|
S_{n-1}
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gptkbp:order
|
(n-1)!
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gptkbp:presentedBy
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<s_i | s_i^2 = 1, (s_i s_{i+1})^3 = 1, (s_i s_j)^2 = 1 for |i-j|>1>
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gptkbp:bfsParent
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gptkb:(n-1)-dimensional_Hamming_cube
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gptkbp:bfsLayer
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7
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