A Combinatorial Characterization of Some Finite Classical Generalized Hexagons

Abstract

We characterize the Moufang hexagons in characteristic 2 by requiring that certain sets of points (defined by distances from other objects) are nonempty. Together with a known result for quadrangles, we obtain a common combinatorial characterization of the symplectic quadrangles over an arbitrary finite field and the classical hexagons over a field of characteristic 2 amongst all finite generalized polygons.