A characterization of buildings of a spherical type
In his article in Eur. J. Comb. 3, 103-118 (1982; Zbl 0504.51006), \textit{F. Buekenhout} provides an axiom system that gives all ''natural'' point- line geometries associated with spherical buildings. The aim of this paper is to simplify his list of axioms. Two main results give necessary and sufficient conditions for the geometry \(\Gamma =({\mathcal P},{\mathcal L})\) to be the geometry of points and lines of a (weak) thick building of one of the given types. The ''only if'' part can be found in literature [see for instance F. Buekenhout, given above, and \textit{A. M. Cohen} and \textit{B. N. Cooperstein}, Geom. Dedicata 15, 73-105 (1983; Zbl 0541.51010)]. The ''if'' part follows immediately by putting together Theorems 3 until 9 of the present article.
scientific article; zbMATH DE number 3979904
scientific article