The classification of endo-trivial modules
نویسندگان
چکیده
منابع مشابه
The classification of torsion endo - trivial modules
This paper settles a problem raised at the end of the seventies by J.L. Alperin [Al1], E.C. Dade [Da] and J.F. Carlson [Ca1], namely the classification of torsion endo-trivial modules for a finite p-group over a field of characteristic p. Our results also imply, at least when p is odd, the complete classification of torsion endo-permutation modules. We refer to [CaTh] and [BoTh] for an overview...
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متن کاملThe group of endo-permutation modules
The group D(P ) of all endo-permutation modules for a finite p-group P is a finitely generated abelian group. We prove that its torsion-free rank is equal to the number of conjugacy classes of non-cyclic subgroups of P . We also obtain partial results on its torsion subgroup. We determine next the structure of Q⊗D(−) viewed as a functor, which turns out to be a simple functor SE,Q , indexed by ...
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Let k be a field of characteristic p, and 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 t...
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The source of a simple kG-module, for a finite p-solvable group G and an algebraically closed field k of prime characteristic p, is an endo-permutation module (see [Pu1] or [Th]). L. Puig has proved, more precisely, that this source must be isomorphic to the cap of an endo-permutation module of the form ⊗ Q/R∈S Ten P Q Inf Q Q/R(MQ/R), where MQ/R is an indecomposable torsion endo-trivial module...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2004
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-004-0385-0