Mathematical Sciences: Groups Acting on Geometries and Graphs

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Fifteen of the 26 sporadic simple groups have now been characterized in terms of flag-transitive actions on k-fold extensions of locally polar spaces and generalized polygons. The problem of classifying these types of geometries is closely related to the problem of classifying 1 - arc transitive graphs with a given local structure. The principal investigator will continue his work in this area and on related problems involving presentations for the sporadic groups, the amalgam method and the Moufang property for generalized polygons. A group is an algebraic structure with a multiplication defined on it. One of the major mathematical accomplishments of the past 15 years was the classification of the finite simple groups. There are 26 exceptional groups, called the sporadic simple groups, which did not fit into the classification scheme. These had to be handled individually. This research is aimed at a unified approach to the sporadic simple groups.