Browsing by Author "Bouc, S."
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Item Open Access Borel-Smith functions and the Dade group(Academic Press, 2007) Bouc, S.; Yalçın, E.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.Item Open Access Monomial G-posets and their Lefschetz invariants(Elsevier, 2019) Bouc, S.; Mutlu, HaticeLet G be a finite group, and C be an abelian group. We introduce the notions of C-monomial G-sets and C-monomial G-posets, and state some of their categorical properties. This gives in particular a new description of the C-monomial Burnside ring BC (G). We also introduce Lefschetz invariants of C-monomial G-posets, which are elements of BC (G). These invariants allow for a definition of a generalized tensor induction multiplicative map TU,λ : BC (G) → BC (H) associated to any C-monomial (G, H)-biset (U, λ), which in turn gives a group homomorphism BC (G)× → BC (H)× between the unit groups of C-monomial Burnside rings.