Statements (33)
Predicate | Object |
---|---|
gptkbp:instanceOf |
gptkb:group_of_people
gptkb:mathematical_concept |
gptkbp:application |
gptkb:Galois_theory
chemistry physics representation theory combinatorics |
gptkbp:category |
gptkb:group_of_people
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 |
19th century
|
gptkbp:generation |
adjacent transpositions
|
https://www.w3.org/2000/01/rdf-schema#label |
symmetric groups
|
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 cycle decomposition simple group permutation transposition |
gptkbp:structure |
non-abelian for n > 2
abelian for n ≤ 2 |
gptkbp:bfsParent |
gptkb:Representation_theory
|
gptkbp:bfsLayer |
5
|