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      Borel-Smith functions and the Dade group

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      Author
      Bouc, S.
      Yalçın, E.
      Date
      2007
      Source Title
      Journal of Algebra
      Print ISSN
      0021-8693
      Electronic ISSN
      1090-266X
      Publisher
      Academic Press
      Volume
      311
      Issue
      2
      Pages
      821 - 839
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      We show that there is an exact sequence of biset functors over p-groups0 → Cb over(→, j) B* over(→, Ψ) DΩ → 0 where Cb is the biset functor for the group of Borel-Smith functions, B* is the dual of the Burnside ring functor, DΩ is the functor for the subgroup of the Dade group generated by relative syzygies, and the natural transformation Ψ is the transformation recently introduced by the first author in [S. Bouc, A remark on the Dade group and the Burnside group, J. Algebra 279 (2004) 180-190]. We also show that the kernel of mod 2 reduction of Ψ is naturally equivalent to the functor B× of units of the Burnside ring and obtain exact sequences involving the torsion part of DΩ, mod 2 reduction of Cb, and B×. © 2006 Elsevier Inc. All rights reserved.
      Keywords
      Borel - Smith functions
      Burnside ring
      Dade group
      Representation rings
      Permalink
      http://hdl.handle.net/11693/23460
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.jalgebra.2006.11.022
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