Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:application |
gptkb:algebraic_geometry
number theory representation theory linear algebra |
| gptkbp:centralTo |
scalar matrices with nonzero determinant
|
| gptkbp:contains |
SL(2, F) as normal subgroup
|
| gptkbp:containsElement |
invertible 2x2 matrices over F
|
| gptkbp:determinant |
homomorphism to F*
|
| gptkbp:field |
F
|
| gptkbp:fullName |
general linear group of degree 2 over F
|
| gptkbp:hasSubgroup |
GL(n, F) for n > 2
|
| https://www.w3.org/2000/01/rdf-schema#label |
GL(2, F)
|
| gptkbp:identityElement |
2x2 identity matrix
|
| gptkbp:isNonAbelian |
true (if |F| > 2)
|
| gptkbp:isQuotientOf |
PGL(2, F)
|
| gptkbp:notation |
GL_2(F)
|
| gptkbp:operator |
matrix multiplication
|
| gptkbp:order |
(q^2-1)(q^2-q) (if F is finite field of order q)
|
| gptkbp:relatedTo |
gptkb:SL(2,_F)
|
| gptkbp:bfsParent |
gptkb:SL(2,_F)
|
| gptkbp:bfsLayer |
6
|