On \(Af.Af^*\) geometries
type: Item
instance of: scholarly article
title: On \(Af.Af^*\) geometries
zbMATH Open document ID: 0840.51005
DOI: 10.1007/BF01222849
author: Antonio Pasini
author: Alberto Del Fra
published in: Journal of Geometry
publication date: 1996-07-07T00:00:00Z
review text: This paper initiates the determination of the flag-transitive rank 3 geometries of type \(L.L^*\) (Buekenhout geometries with a linear diagram and the point-residues are dual linear spaces, the plane-residues are linear spaces). If the (dual) linear spaces are (dual) affine planes, then we have a geometry of type \(Af.Af^*\). It is this special case that has been considered in the paper under review. The authors classify for instance the flag-transitive geometries of type \(Af.Af^*\) of diameter 1. Other partial results are obtained. It is worth mentioning that a lot of properties in this paper do not depend on the flag-transitivity. In that respect, the paper may also be of geometrical and combinatorial interest.
Mathematics Subject Classification ID: 51E24
zbMATH DE Number: 827386
zbMATH Keywords: diagram geometries
zbMATH Keywords: Buekenhout geometries
zbMATH Keywords: flag-transitive geometries
reviewed by: Hendrik Van Maldeghem
MaRDI profile type: Publication
cites work: Q4764158
cites work: Parallelism in diagram geometry
cites work: Q5545191
cites work: Finite rank 3 geometries with affine planes and dual affine point residues
cites work: Four-dimensional football, fullerenes and diagram geometry
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description: scientific article; zbMATH DE number 827386