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      Cohomology of infinite groups realizing fusion systems

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      Author(s)
      Gündoğan, Muhammed Said
      Advisor
      Yalçın, Ergün
      Date
      2019-09
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      Given a fusion system F defined on a p-group S, there exist infinite group models, constructed by Leary and Stancu, and Robinson, that realize F. We study these models when F is a fusion system of a finite group G. If the fusion system is given by a finite group, then it is known that the cohomology of the fusion system and the Fp-cohomology of the group are the same. However, this is not true in general when the group is infinite. For the fusion system F given by finite group G, the first main result gives a formula for the difference between the cohomology of an infinite group model realizing the fusion F and the cohomology of the fusion system. The second main result gives an infinite family of examples for which the cohomology of the infinite group obtained by using the Robinson model is different from the cohomology of the fusion system. The third main result gives a new method for the realizing fusion system of a finite group acting on a graph. We apply this method to the case where the group has p-rank 2, in which case the cohomology ring of the fusion system is isomorphic to the cohomology of the group.
      Keywords
      Fusion systems
      Cohomology of groups
      Cohomology of fusion systems
      Graph of groups
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      http://hdl.handle.net/11693/52444
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      • Dept. of Mathematics - Ph.D. / Sc.D. 48
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