Projective General Linear Group of 3x3 matrices over field K
GPTKB entity
Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
projective linear group |
| gptkbp:abbreviation |
PGL(3, K)
|
| gptkbp:actsOn |
projective plane over K
|
| gptkbp:application |
gptkb:algebraic_geometry
gptkb:geometry group theory |
| gptkbp:builtBy |
General Linear Group GL(3, K)
|
| gptkbp:category |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:centralTo |
trivial
|
| gptkbp:definedIn |
gptkb:field_K
|
| https://www.w3.org/2000/01/rdf-schema#label |
Projective General Linear Group of 3x3 matrices over field K
|
| gptkbp:isQuotientOf |
GL(3, K) modulo scalar matrices
|
| gptkbp:isSimple |
true for most finite fields K except small cases
|
| gptkbp:notation |
gptkb:PGL_3(K)
|
| gptkbp:order |
(q^3-1)(q^3-q)(q^3-q^2)/(q-1)^3 for finite field K=F_q
|
| gptkbp:relatedTo |
Projective Special Linear Group PSL(3, K)
|
| gptkbp:bfsParent |
gptkb:PGL(3,K)
|
| gptkbp:bfsLayer |
8
|