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.

该奖项将支持弗吉尼亚大学的 Leonard Scott 教授与德国斯图加特大学数学与计算机科学学院的 Klaus Roggenkamp 教授进行研究合作。 这些数学家打算研究整数有限群环的一般领域和特征 p 0 的半简单代数群的表示论。更具体地说，他们的目标是研究 Graham Higman 在 1940 年首次提出的同构问题。简单地说，同构问题问的是：“两个整数有限群环的同构何时意味着这些群是 同构？” PI 在解决这一重要问题方面的领导力得到了公正的认可。 1984 年，他们部分地解决了有限幂零群的问题，并且最近为相关的扎森豪斯猜想提供了一个反例。 研究人员现在正处于开发解决该问题所需的技术和工具的阶段，更重要的是，提供一个框架来证明同构问题“通常”有一个肯定的答案。