The Tits Alternative for Groups Defined by Periodic Paired Relations |
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Authors: | Gerald Williams |
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Institution: | 1. Institute of Mathematics, Statistics, and Actuarial Science , University of Kent , Canterbury, Kent, UK g.williams@kent.ac.uk |
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Abstract: | The class of groups defined by periodic paired relations, as introduced by Vinberg, includes the generalized triangle groups, the generalized tetrahedron groups, and the generalized Coxeter groups. We observe that any group defined by periodic paired relations Γ can be realized as a so-called “Pride group”. Using results of Howie and Kopteva we give necessary and sufficient conditions for this Pride group to be non-spherical. Under such conditions, we show that Γ satisfies the Tits alternative. Communicated by A. Olshanskiy |
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Keywords: | Generalized Coxeter group Generalized tetrahedron group Generalized triangle group Group defined by periodic paired relations Pride group Tits alternative |
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