On basis-transitive geometric lattices
type: Item
instance of: scholarly article
title: On basis-transitive geometric lattices
zbMATH Open document ID: 0682.05025
DOI: 10.1016/S0195-6698(89)80073-3
published in: European Journal of Combinatorics
publication date: 1989-01-01T00:00:00Z
review text: The author considers the structure of two- and three-dimensional geometric lattices with a group of automorphisms which operates transitively both on the (unordered) bases and on the points of this lattice. He shows that - with some exceptions - all those lattices are truncations of a Boolean lattice or of an affine or a projective geometry. Thus the author generalizes a theorem of \textit{W. M. Kantor} [J. Comb. Theory, Ser. A 38, 66-74 (1985; Zbl 0559.05015)] on geometry lattices with an automorphism group transitive on ordered bases.
reviewed by: Johannes André
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 51D99
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 4116556
zbMATH Keywords: affine geometry
zbMATH Keywords: geometric lattices
zbMATH Keywords: truncations
zbMATH Keywords: Boolean lattice
zbMATH Keywords: projective geometry
zbMATH Keywords: automorphism group
author: Huiling Li
MaRDI profile type: Publication
cites work: Q5545191
cites work: The Flag-Transitive Collineation Groups of the Finite Desarguesian Affine Planes
cites work: \(k\)-homogeneous groups
cites work: Homogeneous designs and geometric lattices
cites work: Q5617749
cites work: Q5512231
description: scientific article; zbMATH DE number 4116556