Sharply [formula omitted]-transitive groups of projectivities in generalized polygons

Abstract

The group of projectivities of (a line of) a projective plane is always 3-transitive. It is well known that the projective planes with a sharply 3-transitive group of projectivities are classified: they are precisely the Pappian projective planes. It is also well known that the group of projectivities of a generalized polygon is 2-transitive. Here, we classify all generalized quadrangles, all finite generalized hexagons, and the parameter sets of all finite generalized octagons with a sharply 2-transitive group of projectivities.