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

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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.