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Hyperbolic groups of Fibonacci type and T(5) cyclically presented groups

Chinyere, Ihechukwu and Williams, Gerald (2021) 'Hyperbolic groups of Fibonacci type and T(5) cyclically presented groups.' Journal of Algebra, 580. pp. 104-126. ISSN 0021-8693

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Abstract

Building on previous results concerning hyperbolicity of groups of Fibonacci type, we give an almost complete classification of the (non-elementary) hyperbolic groups within this class. We are unable to determine the hyperbolicity status of precisely two groups, namely the Gilbert-Howie groups H(9, 4),H(9, 7). We show that if H(9, 4) is torsion-free then it is not hyperbolic. We consider the class of T(5) cyclically presented groups and classify the (non-elementary) hyperbolic groups and show that the Tits alternative holds.

Item Type: Article
Uncontrolled Keywords: hyperbolic group, Tits alternative, cyclically presented group, Fibonacci group, small cancellation theory
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 07 Apr 2021 18:59
Last Modified: 18 Aug 2022 12:31
URI: http://repository.essex.ac.uk/id/eprint/30164

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