Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
projective linear group |
| gptkbp:actsOn |
projective plane over K
|
| gptkbp:dimensions |
8 (if K is algebraically closed)
|
| gptkbp:fullName |
gptkb:Projective_General_Linear_Group_of_3x3_matrices_over_field_K
|
| https://www.w3.org/2000/01/rdf-schema#label |
PGL(3,K)
|
| gptkbp:isAlgebraicGroup |
true
|
| gptkbp:isMatrixGroup |
true
true if K=R or C |
| gptkbp:isQuotientOf |
gptkb:GL(3,K)
true center of GL(3,K) |
| gptkbp:isSimple |
true for most 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)(q^2-1)(q^3-1) for finite field K=F_q
|
| gptkbp:relatedTo |
gptkb:PSL(3,K)
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:geometry group theory |
| gptkbp:bfsParent |
gptkb:Desarguesian_plane
|
| gptkbp:bfsLayer |
7
|