Rank three geometries associated with \(PSL(3,4)\)
The author constructs three geometries of rank three admitting PSL(3,4) as a flag-transitive automorphism group in a combinatorial way using objects like hyperovals, Baer subplanes and unitals in PG(2,4). These geometries are described by giving their diagrams. Their full automorphism and correlation groups are determined. These geometries are interesting also as examples of building-like geometries in the sense of \textit{F. Buekenhout} and \textit{A. Pasini} [Handbook of incidence geometry, Elsevier (1995; Zbl 0821.00012)] which are extensions of generalized polygons by linear spaces and thick diagram geometries.
scientific article; zbMATH DE number 885635