Groupes de Grothendieck. Introduction

Décompositions de Groupes par Produit Direct et Groupes de Coxeter

We provide examples of groups which are indecomposable by direct product, and more generally which are uniquely decomposable as direct products of indecomposable groups. Examples include Coxeter groups, for which we give an alternative approach to recent results of L. Paris. For a finitely generated linear group Γ, we establish an upper bound on the number of factors of which Γ can be the direc...

Groupes de Galois et nombres automatiques

Description explicite d’une famille de groupes de Kac-Moody affines

For each standard affine data satisfying some condition on the coroots, we define a group functor on the category of all rings which is a subgroup of some group functor R 7→ G(R[t, t−1])o T (R), where G is a Chevalley scheme and T is a torus. This functor is then shown to satisfy the conditions of the five axioms required by [Ti4] to be a ‘minimal’ Kac-Moody group.

Treillis et bases des groupes de Coxeter

A Dominique Foata, pionnier de la combinatoirè a qui elle doit tant 1. Introduction. — Le présent travail est une contributionà l'´ etude de l'ordre fort (dit aussi de Bruhat) dans un groupe de Coxeter fini W. Les définitions et propriétés relatives aux treillis, aux ensembles or-donnés, aux bases et aux treillis enveloppants, &c. sont rassemblées de manì ere minimale dans la section 2, les pre...

Calculs d'invariants primitifs de groupes finis

We introduce in this article a new method to calculate all absolute and relatif primitive invariants of finite groups. This method is inspired from K. Girstmair which calculate an absolute primitive invariant of minimal degree. Are presented two algorithms, the first one enable us to calculate all primitive invariants of minimal degree, and the second one calculate all absolute or relative prim...