Mathematical Sciences: Groups, Algorithms, and Geometries

数学科学：群、算法和几何

• 批准号: 9001784
• 负责人: William Kantor
• 金额: $ 9.64万
• 依托单位: University of Oregon Eugene
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001784&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Groups; Algorithms; Geometries

This research is concerned with probabilistic and generational properties of finite groups. In particular the structure of a random permutation group will be investigated. These results will be applied to algorithmic questions concerning permutation groups. The principal investigator will also consider properties of finite quotients of affine buildings associated with p-adic simple groups. In addition, the relationships among certain generalized quadrangles and certain translation planes will be considered. A group is an algebraic object having a single operation. This work is concerned with determining the generators of a finite group from a probabilistic standpoint. These questions arise directly from desired applications in contemporary computer science.

这项研究涉及有限群的概率和生成特性。特别是随机排列群的结构将被研究。 这些结果将应用于有关排列组的算法问题。主要研究者还将考虑与 p 进简单群相关的仿射建筑物的有限商的性质。此外，还将考虑某些广义四边形和某些平移平面之间的关系。 群是具有单一运算的代数对象。 这项工作涉及从概率的角度确定有限群的生成元。这些问题直接源于当代计算机科学中所需的应用。