### 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 [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.

Original language | English |
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Pages (from-to) | 477-497 |

Number of pages | 20 |

Journal | Journal of Group Theory |

Volume | 6 |

DOIs | |

Publication status | Published - 2003 |

### Cite this

*Journal of Group Theory*,

*6*, 477-497. https://doi.org/10.1515/jgth.2003.033

**Endo-permutation modules as sources of simple modules.** / Mazza, Nadia.

Research output: Contribution to journal › Article

*Journal of Group Theory*, vol. 6, pp. 477-497. https://doi.org/10.1515/jgth.2003.033

}

TY - JOUR

T1 - Endo-permutation modules as sources of simple modules

AU - Mazza, Nadia

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

U2 - 10.1515/jgth.2003.033

DO - 10.1515/jgth.2003.033

M3 - Article

VL - 6

SP - 477

EP - 497

JO - Journal of Group Theory

JF - Journal of Group Theory

SN - 1433-5883

ER -