Classifying geometries with CAYLEY
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.
scientific article; zbMATH DE number 638318