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Endo-permutation modules as sources of simple modules.
The source of a simple -module, for a finite -solvable group and an algebraically closed field of prime characteristic , is an endo-permutation module (see~\cite{Pu1} or~\cite{Th}). L. Puig has proved, more precisely, that this source must be isomorphic to the cap of an endo-permutation module of the form \bigotimes_{Q/R\in\cal S}\Ten^P_Q\Inf^Q_{Q/R}(M_{Q/R}), where is an indecomposable torsion endo-trivial module with vertex , and is a set of cyclic, quaternion and semi-dihedral sections of the vertex of the simple -module. At present, it is conjectured that, if the source of a simple module is an endo-permutation module, then it should have this shape. In this paper, we are going to give a method that allow us to realize explicitly the cap of any such indecomposable module as the source of a simple module for a finite -nilpotent group
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