Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
simple group permutation group |
| gptkbp:centralTo |
trivial for n>2
|
| gptkbp:defines |
the group of even permutations of a finite set of n elements
|
| gptkbp:field |
group theory
|
| gptkbp:for_n=3 |
A_3 is isomorphic to C_3
|
| gptkbp:for_n=4 |
A_4 is not simple
|
| gptkbp:for_n=5 |
A_5 is the smallest non-abelian simple group
|
| gptkbp:for_n>=5 |
A_n is simple
|
| gptkbp:generation |
3-cycles
|
| gptkbp:hasSubgroup |
gptkb:group_of_people
|
| https://www.w3.org/2000/01/rdf-schema#label |
Alternating group
|
| gptkbp:isNonAbelian |
false for n>3
|
| gptkbp:isSolvable |
false for n>=5
|
| gptkbp:namedFor |
gptkb:Évariste_Galois
|
| gptkbp:notation |
A_n
|
| gptkbp:order |
n!/2
|
| gptkbp:relatedTo |
gptkb:group_of_people
projective special linear group sporadic simple groups |
| gptkbp:symbol |
A_n
|
| gptkbp:used_in |
gptkb:algebra
gptkb:Galois_theory mathematical physics combinatorics |
| gptkbp:bfsParent |
gptkb:group_of_people
|
| gptkbp:bfsLayer |
4
|