Geometries of small almost simple groups based on maximal subgroups
For several years, F. Buekenhout and his students are investigating geometries with the aim to find some general pattern which is shared by many geometries for as many as possible sporadic simple groups. The paper under review is a report on a computer search done by the authors for geometries for automorhism groups of \(\text{PSL}(2,q)\), \(4\leq q\leq 19\). Probably, this is the range which is accessible for nowadays computers. All geometries are firm, residually connected, flat transitive and satisfy the rank 2 intersection property. The additional properties the authors are looking for are primitivity (the stabilizer of any object is a maximal subgroup), weak primitivity (the stabilizer of some object is a maximal subgroup) and the corresponding residual properties. The list of geometries runs over 112 pages. The authors claim that it is complete.
scientific article; zbMATH DE number 1260633