Reconstruction of incidence geometries from groups of automorphisms

Abstract

Freudenthal describes a method to construct an incidence geometry from a group such that the given group acts transitively on the set of flags (incident point-line pairs) of the constructed geometry. This method can be found in [5], too. Here we give a useful generalization to geometries that are not flag-homogeneous. Such geometries occur quite naturally in the study of stable planes.