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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~\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 $M_{Q/R}$ is an indecomposable torsion endo-trivial module with vertex $Q/R$, and $\cal S$ is a set of cyclic, quaternion and semi-dihedral sections of the vertex of the simple $kG$-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 $p$-nilpotent group

Year: 2003

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- (1990). Aﬃrmative answer to a question of Feit,
- (1966). Blocks with cyclic defect groups I,
- (1976). Character theory of ﬁnite groups,
- (1998). Character theory of ﬁnite groups, Walter de Gruyter,
- (1978). Endo-permutation modules over p-groups, I, II,
- (1995). evenaz, G-algebras and modular representation theory,
- (1968). Finite groups, Harper and Row,
- (1992). Finite solvable groups, Walter de Gruyter,
- (1981). Methods of representation theory with applications to ﬁnite groups and orders I, Pure and applied mathematics,
- (2000). Non-Additive Exact Functors and Tensor Induction for Mackey Functors,
- (1988). Notes sur les p-alg` ebres de Dade,
- (1978). Repr´ esentation lin´ eaires des groupes ﬁnis,
- (2000). Th´ evenaz, The group of endo-permutation modules,
- (2000). Th´ evenaz, Torsion endo-trivial modules,
- The Dade group of a metacyclic p-group,
- (1982). The Representation Theory of Finite groups,

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