Finite rank 3 geometries with affine planes and dual affine point residues

✍ Scribed by C. Lefevre-Percsy; L. Van Nypelseer

• Publisher: Elsevier Science
• Year: 1990
• Tongue: English
• Weight: 414 KB
• Volume: 84
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(90)90371-n

✦ Synopsis

Let r be a rank 3 incidence geometry of points, lines and planes. This paper classifies all finite geometries r whose planes are affine, whose point residues are dual affine and which satisfy Condition 1: any two points of r are incident with at most one line. Such a geometry is necessarily isomorphic to the incidence structure obtained from any 3-dimensional affine space either by deleting a point and all lines and planes through that point or by deleting a direction of lines and all planes parallel to that direction.