Some combinatorial and geometric characterizations of the finite dual classical generalized hexagons (Q1581007)

The authors characterize the dual of the generalized hexagons naturally associated to the groups \(G_2(q)\) and \({^3D_4}(q)\) by looking at certain configurations and also by considering intersections of traces. For instance, the dual of a generalized hexagon \(\Gamma\) of finite order \((s,t)\) is associated to the Chevalley groups mentioned above if and only if the intersection of any two traces \(x^y\) and \(y^z\) with some additional condition, contains at most \({t\over s}+1\) elements.