Non-Desarguesian Plane

In mathematics, a non-Desarguesian plane, named after Gérard Desargues, is a projective plane that does not satisfy Desargues's theorem, or in other words a plane that is not a Desarguesian plane. The theorem of Desargues is valid in all projective spaces of dimension not 2, that is, all the classical projective geometries over a field (or division ring), but Hilbert found that some projective planes do not satisfy it. Understanding of these examples is not complete, in the current state of knowledge.

Read more about Non-Desarguesian PlaneExamples, Classification

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Non-Desarguesian Plane - Classification
... Lenz classified projective planes in 1954 and this was refined by A ... based on the types of point–line transtitivity permitted by the collineation group of the plane and is known as the Lenz–Barlotti classification of ... known existence results (for both collineation groups and planes having such a collineation group) in both the finite and infinite cases appears on page 126 ...

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