Skip to main content
Article thumbnail
Location of Repository

Endo-permutation modules as sources of simple modules.

By Nadia Mazza

Abstract

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
OAI identifier: oai:eprints.lancs.ac.uk:20816
Provided by: Lancaster E-Prints

Suggested articles

Citations

  1. (1990). Affirmative answer to a question of Feit, doi
  2. (1966). Blocks with cyclic defect groups I, doi
  3. (1976). Character theory of finite groups, doi
  4. (1998). Character theory of finite groups, Walter de Gruyter, doi
  5. (1978). Endo-permutation modules over p-groups, I, II, doi
  6. (1995). evenaz, G-algebras and modular representation theory,
  7. (1968). Finite groups, Harper and Row, doi
  8. (1992). Finite solvable groups, Walter de Gruyter, doi
  9. (1981). Methods of representation theory with applications to finite groups and orders I, Pure and applied mathematics,
  10. (2000). Non-Additive Exact Functors and Tensor Induction for Mackey Functors, doi
  11. (1988). Notes sur les p-alg` ebres de Dade,
  12. (1978). Repr´ esentation lin´ eaires des groupes finis,
  13. (2000). Th´ evenaz, The group of endo-permutation modules, doi
  14. (2000). Th´ evenaz, Torsion endo-trivial modules,
  15. The Dade group of a metacyclic p-group, doi
  16. (1982). The Representation Theory of Finite groups, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.