Borel-Smith functions and the Dade group
Author
Bouc, S.
Yalçın, E.
Date
2007Source 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
ArticleItem Usage Stats
106
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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.