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Décompositions de groupes par produit direct et groupes de Coxeter

Authors
de Cornulier, Yves
Published in Arzhantseva, Goulnara N., Bartholdi, L., Burillo, J., Ventura, E. Geometric group theory : Geneva and Barcelona Conferences. Geneva and Barcelona - June 20th to 25th, 2005 - Basel: Birkhäuser. 2007, p. 75-102
Collection Trends in mathematics
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 Indecomposable groupsDirect productsUniquely directly decomposable groupsCoxeter groupsWedderburn–Remak–Krull–Schmidt theorem
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ISBN: 978-3-7643-8411-1
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DE CORNULIER, Yves, DE LA HARPE, Pierre. Décompositions de groupes par produit direct et groupes de Coxeter. In: Arzhantseva, Goulnara N., Bartholdi, L., Burillo, J., Ventura, E. (Ed.). Geometric group theory : Geneva and Barcelona Conferences. Geneva and Barcelona. Basel : Birkhäuser, 2007. p. 75-102. (Trends in mathematics) https://archive-ouverte.unige.ch/unige:10788

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Deposited on : 2010-08-23

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