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Pré-Publication, Document De Travail Année : 2005

Irreducible Coxeter groups

Résumé

We prove that a non-spherical irreducible Coxeter group is (directly) indecomposable and that a non-spherical and non-affine Coxeter group is strongly indecomposable in the sense that all its finite index subgroups are (directly) indecomposable. We prove that a Coxeter group has a decomposition as a direct product of indecomposable groups, and that such a decomposition is unique up to a central automorphism and a permutation of the factors. We prove that a Coxeter group has a virtual decomposition as a direct product of strongly indecomposable groups, and that such a decomposition is unique up to commensurability and a permutation of the factors.

Dates et versions

hal-00128159 , version 1 (30-01-2007)

Identifiants

Citer

Luis Paris. Irreducible Coxeter groups. 2005. ⟨hal-00128159⟩
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