Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
gptkb:geometry
gptkb:Riemann_sphere projective line |
| gptkbp:defines |
PGL2 is the group of 2x2 invertible matrices over a field K, modulo scalar matrices.
|
| gptkbp:exampleField |
gptkb:PGL(2,_R)
gptkb:PGL(2,_C) PGL(2, F_q) |
| gptkbp:fieldParameter |
K
|
| gptkbp:fullName |
Projective General Linear Group of degree 2
|
| gptkbp:hasSubgroup |
gptkb:PSL2
|
| https://www.w3.org/2000/01/rdf-schema#label |
PGL2
|
| gptkbp:importantFor |
gptkb:algebraic_geometry
gptkb:Galois_theory modular forms number theory automorphic forms |
| gptkbp:isomorphicTo |
PSL2(K) when char(K) ≠ 2 and K has no nontrivial square roots of 1
|
| gptkbp:isQuotientOf |
true
GL2 center of GL2 |
| gptkbp:isSimple |
false
|
| gptkbp:notation |
gptkb:PGL(2)
PGL(2, K) |
| gptkbp:order |
(q^3 - q)/(q-1) for finite field F_q
|
| gptkbp:relatedTo |
gptkb:geometry
gptkb:Möbius_transformations group theory linear algebra |
| gptkbp:usedIn |
classification of finite simple groups
|
| gptkbp:bfsParent |
gptkb:PSL2
|
| gptkbp:bfsLayer |
7
|