symmetric groups

GPTKB entity

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