Mathematical Sciences: Groups Acting on Geometries and Graphs

数学科学：作用于几何和图形的群

• 批准号: 9103552
• 负责人: Richard Weiss
• 金额: $ 3.31万
• 依托单位: Tufts University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103552&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Groups; Acting; Geometries

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.

26个零星单群中的15个现在已经被刻画为局部极空间和广义多边形的k-重扩张上的旗帜传递作用。这些几何类型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。首席调查员将继续他在这一领域的工作以及涉及介绍零星群体、汞齐方法和广义多边形的Moufang性质的相关问题。群是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个例外组，称为零星简单组，不符合分类方案。这些都必须单独处理。本研究旨在为零星的简单群体提供一个统一的研究方法。