Mathematical Sciences: Groups Acting on Geometries and Graphs

26个零星的简单团体中有15个现已被 以k-折叠上的标志传递作用来表征 局部极空间和广义多边形的扩张。 的 分类这些类型的几何形状的问题是密切相关的 与1 -弧传递图的分类问题有关 一个给定的局部结构。 主要研究者将 继续在这一领域和有关问题上开展工作， 关于零星群体、汞合金法和 广义多边形的Moufang性质。 群是一个代数结构， 数学的主要成就之一 过去的15年是有限简单的分类， 组 有26个特殊的群体，称为零星的 简单的群体，不适合分类方案。 这些必须单独处理。 本研究的目的是 一个统一的方法，零星的简单的群体。

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.