A characterization of special Laguerre planes and extended dual affine planes
type: Item
instance of: scholarly article
title: A characterization of special Laguerre planes and extended dual affine planes
zbMATH Open document ID: 0549.51004
author: Alan P. Sprague
published in: Geometriae Dedicata
publication date: 1984-01-01T00:00:00Z
review text: The author proves the following theorem: Let \(\rho\) be a nondegenerate finite connected incidence structure. Let the residue of each point be a dual affine plane. Then either \(\rho\) is an extended dual affine plane or \(\rho\) is a special Laguerre plane. Here an extended dual plane is an incidence structure such that the residue of each point is a dual affine plane, and each pair of points os in at least one block. (Finite extended dual affine planes exist only of order 2,4 and (dubiously) 10). A special Laguerre plane is a nondegenerate transversal 3-design such that the residue of each point is a dual affine plane. Special Laguerre planes are equivalent to certain codes.
Mathematics Subject Classification ID: 51E05
Mathematics Subject Classification ID: 51A05
zbMATH DE Number: 3876066
zbMATH Keywords: extended dual affine plane
zbMATH Keywords: special Laguerre plane
zbMATH Keywords: transversal 3-design
zbMATH Keywords: codes
reviewed by: Wolfgang Nolte
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3876066