finite simple groups of Lie type
GPTKB entity
Statements (53)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
group family
|
| gptkbp:class |
gptkb:Steinberg_groups
gptkb:Chevalley_groups exceptional groups part of classification of finite simple groups twisted groups |
| gptkbp:example |
gptkb:PSL(2,7)
gptkb:PSL(3,2) gptkb:Tits_group gptkb:G2(2) PSU(3,3) PSp(4,3) Ree group 2G2(3^2n+1) Suzuki group Sz(8) |
| gptkbp:excludes |
Tits group is not simple
|
| gptkbp:hasApplication |
gptkb:geometry
gptkb:mathematics gptkb:theoretical_physics coding theory combinatorics |
| gptkbp:hasProperty |
simple
finite non-abelian arise from algebraic groups over finite fields |
| gptkbp:hasType |
classical groups
exceptional groups twisted groups untwisted groups |
| https://www.w3.org/2000/01/rdf-schema#label |
finite simple groups of Lie type
|
| gptkbp:includes |
gptkb:Steinberg_groups
gptkb:Chevalley_groups gptkb:Suzuki_groups gptkb:exceptional_groups_of_Lie_type gptkb:Tits_group Ree groups twisted groups of Lie type projective orthogonal groups PΩ(n,q) projective special linear groups PSL(n,q) projective special unitary groups PSU(n,q) projective symplectic groups PSp(2n,q) |
| gptkbp:namedAfter |
gptkb:Wilhelm_Killing
gptkb:Élie_Cartan |
| gptkbp:order |
order depends on type and field size
|
| gptkbp:originatedIn |
constructed from simple algebraic groups over finite fields
|
| gptkbp:studiedIn |
gptkb:algebra
group theory finite group theory |
| gptkbp:subclassOf |
gptkb:Weyl_group
gptkb:group_of_people |
| gptkbp:bfsParent |
gptkb:Suzuki_groups
gptkb:PSL_n(q) gptkb:finite_simple_groups_PSL(2,p) |
| gptkbp:bfsLayer |
7
|