Borel-Smith functions and the Dade Group
Journal of Algebra
Bouc, S., & Yalçın, E. (2007). Borel–Smith functions and the Dade group. Journal of Algebra, 311(2), 821-839.
Please cite this item using this persistent URLhttp://hdl.handle.net/11693/11589
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