Statements (45)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
simple group permutation group |
| gptkbp:A_1 |
trivial group
abelian isomorphic to trivial group |
| gptkbp:A_2 |
trivial group
abelian isomorphic to trivial group |
| gptkbp:A_3 |
cyclic group of order 3
abelian isomorphic to cyclic group of order 3 |
| gptkbp:A_4 |
not simple
group of order 12 has normal subgroup of order 4 isomorphic to group of even permutations of 4 elements |
| gptkbp:A_5 |
simple group of order 60
isomorphic to PSL(2,5) isomorphic to icosahedral group isomorphic to rotation group of dodecahedron isomorphic to rotation group of icosahedron smallest non-abelian simple group |
| gptkbp:A_6 |
has outer automorphism
not a complete group order 360 |
| gptkbp:A_7 |
order 2520
|
| gptkbp:A_8 |
order 20160
|
| gptkbp:centralTo |
trivial group (for n > 2)
|
| gptkbp:consistsOf |
even permutations
|
| gptkbp:definedIn |
set of n elements
|
| gptkbp:generation |
3-cycles
|
| gptkbp:hasNormalSubgroup |
gptkb:symmetric_group_S_n
|
| gptkbp:hasSubgroup |
gptkb:symmetric_group_S_n
|
| https://www.w3.org/2000/01/rdf-schema#label |
alternating group A n
|
| gptkbp:isNonAbelian |
false (for n > 2)
|
| gptkbp:isSimple |
n >= 5
|
| gptkbp:namedAfter |
alternating permutations
|
| gptkbp:notation |
A_n
|
| gptkbp:order |
n!/2
|
| gptkbp:usedIn |
gptkb:algebra
gptkb:Galois_theory group theory combinatorics |
| gptkbp:bfsParent |
gptkb:symmetric_group_S_n
|
| gptkbp:bfsLayer |
6
|