Mathematical Sciences: Groups Acting on Geometries and Graphs

从局部极空间和广义多边形的k-fold扩展上的旗子传递作用的角度对26个偶发单群中的15个进行了表征。这类几何的分类问题与具有给定局部结构的1 -弧传递图的分类问题密切相关。主要研究者将继续他在这一领域的工作，并在相关问题上涉及零星群的介绍，汞合金方法和广义多边形的牟方性质。群是在其上定义了乘法的代数结构。过去15年的主要数学成就之一是有限单群的分类。有26个特殊的类群，被称为零星的简单类群，它们不适合分类方案。这些必须单独处理。本研究的目的是统一的方法，以零星的简单群体。

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.