Truncations of inductively minimal geometries

Abstract

AbstractInductively minimal geometries form an infinite family of incidence geometries on which finite symmetric groups act flag-transitively. They were introduced in Buekenhout et al. (in: N.L. Johnson (Ed.), Mostly Finite Geometries, Marcel Dekker, New York, 1997, pp. 185–190) and satisfy, among other, the (IP)2 and RWPRI conditions (see Bull. Belg. Math. Soc. Simon Stevin 5 (1998) 213–219). In the present paper we characterize the truncations of inductively minimal geometries which satisfy both of these conditions. We also determine all rank 2 residues in these truncations. This enables one to find the diagram of these truncations