Characterizations

Abstract

The main question of this chapter is: “how do we recognize the Moufang polygons?”. Of course, checking the Moufang condition is one answer, but in a lot of cases, other criteria are needed. From a geometric point of view for instance, one would like to identify Moufang polygons by certain geometric or, in the finite case, combinatorial properties. This also means that, in the case of generalized ngons, n ∉ {3, 4, 6, 8}, we would like to have geometric properties eliminating these geometries, analogous to the result of Tits [1976b], [1979] and Weiss [1979] (see Theorem 5.3.4 on page 185).