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Concept

Groupe de Prüfer

Publications associées (20)

On the lifting of the Dade group

Jacques Thévenaz, Caroline Lassueur

For the group of endo-permutation modules of a finite p-group, there is a surjective reduction homomorphism from a complete discrete valuation ring of characteristic 0 to its residue field of characteristic p. We prove that this reduction map always has a ...

2019

An Ergodic Theory of Binary Operations-Part II: Applications to Polarization

Rajai Nasser

An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Arikan style constructions. This paper, which is presented in two parts, solves this probl ...

Institute of Electrical and Electronics Engineers2017

SETS OF p-UNIQUENESS ON NONCOMMUTATIVE LOCALLY COMPACT GROUPS

Antoine Derighetti

We prove that a closed subgroup H of a locally compact group G is a set of p-uniqueness (1 < p < infinity) if and only if H is locally negligible. We also obtain the inverse projection theorem for sets of p-uniqueness. ...

Ars Polona-Ruch2017

Spaces With Noetherian Cohomology

Jérôme Scherer

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? In this paper we provide, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov Theorem. W ...

Cambridge University Press2013

The Dade group of a finite group

Caroline Lassueur

The aim of this paper is to construct an equivalent of the Dade group of a p-group for an arbitrary finite group G, whose elements are equivalences classes of endo-p-permutation modules. To achieve this goal we use the theory of relative projectivity with ...

Elsevier2013

Relative Projectivity and Relative Endotrivial Modules

Caroline Lassueur

This dissertation is concerned with modular representation theory of finite groups, and more precisely, with the study of classes of representations, which we shall term relative endotrivial modules. Given a prime number p, a finite group G of order divisi ...

EPFL2012

Stabilizing bisets

Jacques Thévenaz, Serge Bouc

Let G be a finite group and let R be a commutative ring. We analyse the (G,G)-bisets which stabilize an indecomposable RG-module. We prove that the minimal ones are unique up to equivalence. This result has the same flavor as the uniqueness of vertices and ...

2012

Le foncteur de bi-ensembles des modules de p-permutation

Mélanie Baumann

Let k be an algebraically closed field of characteristic p, where p is a prime number or 0. Let G be a finite group and ppk(G) be the Grothendieck group of p-permutation kG-modules. If we tensor it with C, then Cppk becomes a C-linear biset functor. Recall ...

EPFL2012

Elementary abelian subgroups in p-groups with a cyclic derived group

Let p be an arbitrary prime and let P be a finite p-group. The general objective of this paper is to obtain refined information on the homotopy type of the poset of all non-trivial elementary abelian subgroups of P, ordered by inclusion, and the poset of a ...

Elsevier2011

Relative projectivity and relative endotrivial modules

Caroline Lassueur

In this paper, we use projectivity relative to kG-modules to define groups of relatively endotrivial modules, which are obtained by replacing the notion of projectivity with that of relative projectivity in the definition of ordinary endotrivial modules. T ...

Elsevier2011

Elementary abelian subgroups in p-groups of class 2

All the results in this work concern (finite) p-groups. Chapter 1 is concerned with classifications of some classes of p-groups of class 2 and there are no particularly new results in this chapter, which serves more as an introductory chapter. The "geometr ...

EPFL2009

The socle of a projective Mackey functor for a p-group

We study the simple subfunctors of indecomposable projective Mackey functors for a p-group P. Unlike the case of group algebras, the Mackey algebra is not in general self-injective. Thus, the socle of an indecomposable projective functor is not in general ...

2009

Extension groups between simple Mackey functors

In order to better understand the structure of indecomposable projective Mackey functors, we study extension groups of degree 1 between simple Mackey functors. We explicitly determine these groups between simple functors indexed by distinct normal subgroup ...

2009

Gluing torsion endo-permutation modules

Jacques Thévenaz, Serge Bouc

Given a finite p-group P, the main result gives necessary and sufficient conditions for obtaining a torsion endo-permutation module for P by gluing a compatible family of torsion endo-permutation modules for all sections N(Q)/Q, where Q runs among non-triv ...

2008

A sectional characterization of the Dade group

Jacques Thévenaz, Serge Bouc

Let k be a field of characteristic p, let P be a finite p-group, where p is an odd prime, and let D(P) be the Dade group of endo-permutation kP-modules. It is known that D(P) is detected via deflation-restriction by the family of all sections of P which ar ...

2008

Foncteurs de Mackey projectifs

This work deals with the study of projective Mackey functors. Mackey functors are algebraic structures with operations which behave like induction, restriction and conjugation in group representation theory. These objects have properties which generalize m ...

EPFL2008

On the essential dimension of cyclic p-groups

Let p be a prime number, let K be a field of characteristic not p, containing the p-th roots of unity, and let r >= 1 be an integer. We compute the essential dimension of Z/p(r) Z over K (Theorem 4.1). In particular, i) We have edℚ(ℤ/8ℤ)=4, a result which ...

Springer-Verlag2008

Endotrivial modules in the cyclic case

Jacques Thévenaz

We determine all endotrivial modules in prime characteristic p, for a finite group having a cyclic Sylow p-subgroup. In other words, we describe completely the group of endotrivial modules in that case. ...

2007

Modules d'endo-p-permutation

Jean-Marie Urfer

This dissertation is concerned with the study of a new family of representations of finite groups, the endo-p-permutation modules. Given a prime number p, a finite group G of order divisible by p and an algebraically closed field k of characteristic p, we ...

EPFL2006

The classification of torsion endo-trivial modules

Jacques Thévenaz

The main purpose of this paper is to show that, if G is a finite p-group which is not cyclic, quaternion or semi-dihedral, then the group of endo-trivial G-modules is detected on restriction to elementary abelian p-subgroups of rank 2. Consequently, the to ...

2005

Publications associées (20)