On C2.L-geometries

Abstract

A C2.L-geometry is a geometry of rank 3 with elements called points, lines and quads, where residues of points are linear spaces, residues of lines are generalized digons and residues of quads are generalized quadrangles. Some sufficient conditions can be found in the literature for a C2.L-geometry to be a quotient of a truncated Cn-building. We shall weaken those conditions in this paper.