U.S.- Federal Republic of Germany Cooperative Research in Mathematics: The Isomorphism Problem for Finite Group Rings

美德数学合作研究：有限群环的同构问题

• 批准号: 8912628
• 负责人: Leonard Scott
• 金额: $ 1.5万
• 依托单位: University of Virginia Main Campus
• 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: 1990-08-01 至 1994-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8912628&HistoricalAwards=false
• 关键词: U.S.; Federal; Republic; Germany; Cooperative

This award will support Professor Leonard Scott of the University of Virginia in a research collaboration with Professor Klaus Roggenkamp of the Faculty of Mathematics and Computer Science at the University of Stuttgart, Germany. These mathematicians intend to work on the general area of integral finite group rings and the representation theory of semisimple algebraic groups in characteristic p 0. More specifically, they aim to work on the isomorphism problem first posed by Graham Higman in 1940. Briefly stated, the isomorphism problem asks, "when does an isomorphism of two integral finite group rings imply the groups are isomorphic?" The PI's are justly recognized for their leadership in attacking this important problem. In 1984 they partially solved the problem in the affirmative for finite nilpotent groups and recently provided a counter-example to the related Zassenhaus conjecture. The investigators are now at the stage where they have developed the techniques and tools necessary to resolve the problem and, more important, to provide a framework for proving that the isomorphism problem "usually" has a positive answer.

这个奖项将支持教授伦纳德斯科特的 弗吉尼亚大学与 数学系教授克劳斯·罗根坎普和 德国斯图加特大学计算机科学系。 这些数学家打算在一般领域的工作， 整有限群环及其表示理论 特征p 0的半单代数群 更 具体来说，他们的目标是解决同构问题， 第一次提出是在1940年。 简而言之， 同构问题问，“什么时候两个同构 整数有限群环意味着群是同构的？" PI的公正承认他们的领导， 解决这个重要问题。 1984年，部分 解决了有限幂零的肯定问题 集团，最近提供了一个反例，以有关 扎森豪斯猜想 调查人员目前正在 他们已经开发出技术和工具的阶段 解决这个问题，更重要的是， 提供了一个框架来证明同构问题 “通常”的答案是肯定的