Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
set of n elements
|
| gptkbp:automorphismGroup |
set of n elements
|
| gptkbp:centralTo |
trivial (if n>2)
|
| gptkbp:contains |
gptkb:A_n_(alternating_group)
|
| gptkbp:field |
group theory
|
| gptkbp:generation |
transpositions
|
| gptkbp:hasConjugacyClasses |
indexed by partitions of n
|
| gptkbp:hasElementOrder |
any divisor of n!
|
| gptkbp:hasIrreducibleRepresentations |
indexed by partitions of n
|
| gptkbp:hasSubgroup |
A_n
itself |
| https://www.w3.org/2000/01/rdf-schema#label |
S n
|
| gptkbp:isCayleyGroup |
true
|
| gptkbp:isDirectProduct |
no
|
| gptkbp:isFinite |
true
|
| gptkbp:isGroupOfPermutations |
true
|
| gptkbp:isNonAbelian |
true (if n>=3)
|
| gptkbp:isPermutationGroup |
true
|
| gptkbp:isSimple |
true (if n=2 or n>=5)
|
| gptkbp:isSolvable |
false (if n>=5)
true (if n<=4) |
| gptkbp:isTransitiveOn |
true
|
| gptkbp:isWreathProduct |
no
|
| gptkbp:notation |
Sym(n)
|
| gptkbp:order |
n!
|
| gptkbp:bfsParent |
gptkb:group_of_people
|
| gptkbp:bfsLayer |
4
|