Classifying geometries with CAYLEY
type: Item
instance of: scholarly article
title: Classifying geometries with CAYLEY
zbMATH Open document ID: 0824.51009
author: Michel Dehon
published in: Journal of Symbolic Computation
publication date: 1994-10-13T00:00:00Z
review text: Well-known after Tits, there is a standard way to define a geometry from a group and a collection of subgroups. [See also: `Handbook of Incidence Geometry' by \textit{F. Buekenhout}, North-Holland (1995; Zbl 0821.00012), Chapter 3]. The aim of this paper is to present a set of Cayley programs that can be used to classify all the primitive, firm, residually connected and flag- transitive geometries associated with a given group \(G\). The author starts from a particular classification of geometries by Hermand and Buekenhout, with the help of Cayley (Preprint 1994 by Buekenhout and Hermand). As an interesting application the classification for the group \(W(E_ 6)\) of order 51 840 is described.
reviewed by: Erhard Quaisser
Mathematics Subject Classification ID: 51E24
Mathematics Subject Classification ID: 20E42
zbMATH DE Number: 638318
zbMATH Keywords: incidence geometry
zbMATH Keywords: Cayley program
MaRDI profile type: Publication
full work available at URL: jsco.1994.1016
OpenAlex ID: W1986902553
DOI: 10.1006/JSCO.1994.1016
description: scientific article; zbMATH DE number 638318