Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
simple group |
| gptkbp:automorphismGroup |
trivial for n-1 ≠ 6
order 4 for n-1 = 6 |
| gptkbp:centralTo |
trivial group
|
| gptkbp:defines |
group of even permutations on n-1 elements
|
| gptkbp:generation |
3-cycles
|
| gptkbp:hasNormalSubgroup |
gptkb:symmetric_group_S_{n-1}
|
| gptkbp:hasSubgroup |
gptkb:symmetric_group_S_{n-1}
|
| https://www.w3.org/2000/01/rdf-schema#label |
alternating group A {n-1}
|
| gptkbp:isNonAbelian |
false
|
| gptkbp:isNonabelianSimple |
true for n-1 > 4
|
| gptkbp:isPerfect |
true
|
| gptkbp:isPrimitive |
true for n-1 > 2
|
| gptkbp:isQuotientOf |
special linear group SL_{n-1}(F_2) for n-1=8
|
| gptkbp:isSimple |
n-1 > 4
|
| gptkbp:isTransitiveOn |
true
|
| gptkbp:minimalDegreeOfFaithfulPermutationRepresentation |
n-1
|
| gptkbp:notation |
A_{n-1}
|
| gptkbp:order |
(n-1)!/2
|
| gptkbp:bfsParent |
gptkb:symmetric_group_S_{n-1}
|
| gptkbp:bfsLayer |
8
|