Gluing torsion endo-permutation modules

• Autores: Serge Bouc, Jacques Thévenaz
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 78, Nº 2, 2008, págs. 477-501
• Idioma: inglés
• DOI: 10.1112/jlms/jdn039
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• Resumen

  • Let k be a field of characteristic p, and let P be a finite p-group, where p is an odd prime. In this paper, we consider the problem of gluing compatible families of endo-permutation modules: being given a torsion element MQ in the Dade group D(NP(Q)/Q), for each non-trivial subgroup Q of P, subject to obvious compatibility conditions, we show that it is always possible to find an element M in the Dade group of P such that for all Q, but that M need not be a torsion element of D(P). The obstruction to this is controlled by an element in the zeroth cohomology group over 2 of the poset of elementary abelian subgroups of P of rank at least 2. We also give an example of a similar situation, when MQ is only given for centric subgroups Q of P. Moreover, general results about biset functors and the Dade functor are given in two appendices