Extended dual affine planes
type: Item
instance of: scholarly article
title: Extended dual affine planes
zbMATH Open document ID: 0546.51008
author: Alan P. Sprague
published in: Geometriae Dedicata
publication date: 1984-01-01T00:00:00Z
review text: The author studies rank 3 diagram geometries such that the residue of a point is a dual net and the residue of a plane is linear. Examples of these geometries include extended dual affine planes, Laguerre planes, 3- nets, and orthogonal arrays of strength 3. He proves that any such finite geometry satisfying Buekenhout's intersection property, and such that any two points are coplanar, is an extended dual affine plane (and so has order 2,4 or 10). Furthermore he shows that this geometry may be embedded in an extended projective plane of the same order. By a free construction he shows that the last result is false if the geometry is infinite. \(\{\) Reviewers remark. By a recent result due to G. Faina there is no extended projective plane of order 10. Hence the order 10 in the theorem above cannot occur.\(\}\)
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 3870098
zbMATH Keywords: rank 3 diagram geometries
zbMATH Keywords: extended dual affine planes
zbMATH Keywords: Laguerre planes
zbMATH Keywords: 3-nets
zbMATH Keywords: orthogonal arrays of strength 3
zbMATH Keywords: Buekenhout's intersection property
reviewed by: Gernot Stroth
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3870098