Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:abelianFor |
n < 3
|
| gptkbp:centralTo |
trivial (identity only) for n > 2
|
| gptkbp:containsElement |
even permutation
|
| gptkbp:definedIn |
the group of even permutations on n elements
|
| gptkbp:generation |
3-cycles
|
| gptkbp:hasSubgroup |
S_n (symmetric group)
|
| https://www.w3.org/2000/01/rdf-schema#label |
A n (symmetric group)
|
| gptkbp:indexIn |
2 in S_n (symmetric group)
|
| gptkbp:isomorphicTo |
Klein four-group for n=4
|
| gptkbp:isQuotientOf |
trivial group for n < 5
|
| gptkbp:isSimple |
n >= 5
|
| gptkbp:namedAfter |
gptkb:group_of_people
|
| gptkbp:non-abelianFor |
n >= 3
|
| gptkbp:normalSubgroupOf |
S_n (symmetric group)
|
| gptkbp:notation |
A_n
|
| gptkbp:notSimpleFor |
n=4
|
| gptkbp:order |
n!/2
|
| gptkbp:trivialFor |
n < 2
|
| gptkbp:usedIn |
gptkb:algebra
gptkb:mathematics gptkb:Galois_theory group theory combinatorics |
| gptkbp:bfsParent |
gptkb:Coxeter_groups
|
| gptkbp:bfsLayer |
7
|