Efficient Computation in Finite Groups

有限群中的高效计算

• 批准号: 9201303
• 负责人: Akos Seress
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-15 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201303&HistoricalAwards=false
• 关键词: Efficient; Computation; Finite; Groups

This project will investigate efficient manipulation of finite groups and estimation of their parameters. The main focus is on the design and analysis of efficient algorithms for large group-theoretic problems. While interested in improved asymptotic performance, the project will also emphasize practicability, demonstrating the relevance of the asymptotic paradigm to efficient implementation. Of interest also is the development of parallel versions of the algorithms. The investigation will be extended to matrix groups, the most frequently occurring representations of finite groups. Finally, the project will investigate important parameters of groups, especially the estimation of diameters of various classes of Cayley graphs.

这个项目将研究有限群的有效操作和它们的参数估计。主要的焦点是设计和分析大型群论问题的高效算法。在对改进的渐近性能感兴趣的同时，该项目还将强调实用性，展示渐近范例与有效实施的相关性。令人感兴趣的还有算法的并行版本的开发。研究将扩展到矩阵群，这是有限群最常见的表示。最后，本项目将研究群的重要参数，特别是各类Cayley图的直径估计。