Decompositions de groupes par produit direct et groupes de Coxeter

Abstract

We provide examples of groups which are indecomposable by direct product, and more generally which are uniquely decomposable in 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 Gamma, we establish an upper bound on the number of factors of which Gamma can be the direct product. If Gamma is moreover torsion-free, it follows that Gamma is uniquely decomposable in direct product of indecomposable groups.