Moufang Polygons

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9801194 Weiss In 1974, Jacques Tits Classified buildings of spherical type which are of rank at least three. Generalized polygons are spherical buildings of rank two. The generalized polygons which are spherical buildings of classical and algebraic simple groups of Lie rank two all satisfy the Moufang property. Tits and the principal investigator have recently classified Moufang polygons. The principal investigator will investigate various questions which arise out of this work. The most important of these concern the existence and structure of the exceptional quadrangles. The research in this project involves the interplay between finite geometry and the actions of groups of transformations on these geometries. This work has implications for the structure of finite groups, for algebraic coding theory, and for finite geometry.