Statements (34)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:mathematical_concept |
| gptkbp:application |
gptkb:combinatorics
gptkb:Galois_theory chemistry physics representation theory |
| gptkbp:category |
gptkb:group_of_people
gptkb:permutation_group |
| gptkbp:centralTo |
trivial for n > 2
|
| gptkbp:contains |
gptkb:group_of_people
|
| gptkbp:defines |
group of all permutations of a finite set
|
| gptkbp:field |
abstract algebra
group theory |
| gptkbp:firstAppearance |
gptkb:19th_century
|
| gptkbp:generation |
adjacent transpositions
|
| gptkbp:isSolvable |
for n ≤ 4
|
| gptkbp:namedFor |
gptkb:Augustin-Louis_Cauchy
|
| gptkbp:notation |
gptkb:S_n
|
| gptkbp:notSolvable |
for n ≥ 5
|
| gptkbp:order |
n!
|
| gptkbp:relatedTo |
gptkb:group_of_people
gptkb:Young_tableau gptkb:Cayley's_theorem gptkb:simple_group cycle decomposition permutation transposition |
| gptkbp:structure |
non-abelian for n > 2
abelian for n ≤ 2 |
| gptkbp:bfsParent |
gptkb:Hecke_algebra
gptkb:Representation_theory |
| gptkbp:bfsLayer |
7
|
| https://www.w3.org/2000/01/rdf-schema#label |
symmetric groups
|