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Talks

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Talks 2018

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1 entries found

  • January
  • 18. January
    17:00 - 18:00
    Location: 48-436
    AG Algebra, Geometrie und Computer Algebra

    Florian Eisele, University of London: A counterexample to the first Zassenhaus conjecture

    There are many interesting problems surrounding the unit group U(RG) of the ring RG, where R is a commutative ring and G is a finite group. Of particular interest are the finite subgroups of U(RG). In the seventies, Zassenhaus conjectured that any u in U(ZG) is conjugate, in the group U(QG), to an element of the form +/-g, where g is an element of the group G. This came to be known as the "Zassenhaus conjecture". In recent joint work with L. Margolis, we were able to construct a counterexample to this conjecture. In this talk I will give an introduction to the various conjectures surrounding finite subgroups of U(RG), and how they can be reinterpreted as questions on the (non-)existence of certain R(GxH)-modules, where H is another finite group. This establishes a link with the representation theory of finite groups, and I will explain how, p-locally, our example is made up of certain p-permutation modules.