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The Tits alternative for Groups defined by Periodic Paired Relations

Williams, G (2006) 'The Tits alternative for Groups defined by Periodic Paired Relations.' Communications in Algebra, 34 (4). pp. 251-258. ISSN 0092-7872

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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 Gamma 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 Gamma satisfies the Tits alternative.

Item Type: Article
Uncontrolled Keywords: Generalized Coxeter group; Generalized tetrahedron group; Generalized triangle group; Group defined by periodic paired relations; Pride group; Tits alternative
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 25 May 2012 09:56
Last Modified: 06 Jan 2022 13:27
URI: http://repository.essex.ac.uk/id/eprint/2405

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