Premium
Gluing torsion endo‐permutation modules
Author(s) -
Bouc Serge,
Thévenaz Jacques
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdn039
Subject(s) - mathematics , functor , torsion (gastropod) , combinatorics , abelian group , cohomology , pure mathematics , discrete mathematics , medicine , surgery
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 M Q in the Dade group D ( N P ( 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 Defre s N P ( Q ) / Q P M = M Qfor 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 M Q is only given for centric subgroups Q of P . Moreover, general results about biset functors and the Dade functor are given in two appendices.