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Décompositions de Groupes par Produit Direct et Groupes de Coxeter

  • Yves de Cornulier
  • Pierre de la Harpe
Part of the Trends in Mathematics book series (TM)

Abstract

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 direct product. If moreover Γ has a finite centre or a finite abelianization, it follows that Γ is uniquely decomposable as direct product of indecomposable groups.

Keywords

Nous Avons Coxeter Group Uniquement Directement Coxeter System Direct Product Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Yves de Cornulier
    • 1
  • Pierre de la Harpe
    • 2
  1. 1.IRMARRennes CedexFrance
  2. 2.Section de MathématiquesUniversité de GenèveGenève 4

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