GENERALIZED HEXAGONS AS AMALGAMATIONS OF GENERALIZED QUADRANGLES

We define the notion of regular point p in a generalized hexagon and show how a derived geometry at such a point can be defined. We motivate this by proving that, for finite generalized hexagons of order (s, t), this derivation is a generalized quadrangle iff s = t. Moreover, if the generalized hexagon has also a regular line incident with p, then one can amalgamate the two corresponding generalized quadrangles and in this way reconstruct the generalized hexagon. The small Moufang hexagons of order 3h, for small h, are characterized in this manner. © 1993 Academic Press, Inc.