Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
projective plane
|
| gptkbp:automorphismGroup |
gptkb:PGL(3,K)
|
| gptkbp:canCreate |
vector space over division ring
|
| gptkbp:dimensions |
2
|
| gptkbp:heldBy |
gptkb:classical_projective_plane
all finite projective planes of order ≤ 8 are Desarguesian PG(2,2) is the smallest Desarguesian plane PG(2,K) for division ring K PG(2,q) for finite field F_q all projective planes of order 9 are Desarguesian except one (the Hall plane) coordinatizable projective plane finite if K is finite infinite if K is infinite not all projective planes are Desarguesian unique up to isomorphism for each division ring K used in algebraic geometry used in combinatorics used in finite geometry used in incidence geometry all projective planes of order 2, 3, 4, 5, 7, 8 are Desarguesian |
| https://www.w3.org/2000/01/rdf-schema#label |
Desarguesian plane
|
| gptkbp:isomorphicTo |
gptkb:projective_geometry_PG(2,K)
projective plane over a field |
| gptkbp:namedAfter |
gptkb:Gérard_Desargues
|
| gptkbp:order |
q if K is finite field of order q
|
| gptkbp:satisfies |
gptkb:Desargues'_theorem
|
| gptkbp:bfsParent |
gptkb:Moufang_plane
|
| gptkbp:bfsLayer |
6
|