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Geometric Group Theory pp 75–102Cite as

Décompositions de Groupes par Produit Direct et Groupes de Coxeter

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Part of the book series: Trends in Mathematics ((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.

This article originates from the Geneva conference.

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Author information

Authors and Affiliations

  1. IRMAR, Campus de Beaulieu, F-35042, Rennes Cedex, France

    Yves de Cornulier

  2. Section de Mathématiques, Université de Genève, C.P. 64, CH-1211, Genève 4

    Pierre de la Harpe

Authors
  1. Yves de Cornulier
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  2. Pierre de la Harpe
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Editor information

Editors and Affiliations

  1. Section de mathématiques, Université de Genève, 2-4, rue du Lièvre, Case postale 64, 1211, Genève 4, Switzerland

    Goulnara N. Arzhantseva

  2. Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya Escola Politècnica Superior de Castelldefels Avda, Del Canal Olímpic s/n, 08860, Castelldefels (Barcelona), Spain

    José Burillo

  3. Institut de Mathématiques B (IMB), École Polytechnique Fédérale de Lausanne (EPFL), 1015, Lausanne, Switzerland

    Laurent Bartholdi

  4. Department of Applied Mathematics III Escola Politècnica Superior d’Enginyeria de Manresa, Universitat Politècnica de Catalunya, Av.Bases de Manresa 61-73, 08242, Manresa / Barcelona, Spain

    Enric Ventura

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© 2007 Birkhäuser Verlag Basel/Switzerland

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de Cornulier, Y., de la Harpe, P. (2007). Décompositions de Groupes par Produit Direct et Groupes de Coxeter. In: Arzhantseva, G.N., Burillo, J., Bartholdi, L., Ventura, E. (eds) Geometric Group Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8412-8_7

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