Endo-permutation modules as sources of simple modules

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 [13] or [16]). L. Puig has proved, more precisely, that this source must be isomorphic to the cap of an endo-permutation module of the form x(Q/ReL)Ten(Q)(P)Inf(Q/R)(Q) (M-Q/R), where M-Q/R is an indecomposable torsion endo-trivial module with vertex Q/R, and L is a set of cyclic, quaternion and semi-dihedral sections of the vertex of the simple kG-module. It is conjectured that, if the source of a simple module is an endo-permutation module, then it must have this form. In this paper, we give a method for realizing explicitly the cap of any such indecomposable module as the source of a simple module for a finite p-nilpotent group.