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The Tits alternative for generalized triangle groups of type (3, 4, 2)

Howie, J and Williams, G (2008) 'The Tits alternative for generalized triangle groups of type (3, 4, 2).' Algebra and Discrete Mathematics, 2008 (4). 40 - 48.

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Abstract

A generalized triangle group is a group that can be presented in the form G = h x, y | xp = yq = w(x, y)r = 1 i where p, q, r ? 2 and w(x, y) is a cyclically reduced word of length at least 2 in the free product Zp ? Zq = h x, y | xp = yq = 1i. Rosenberger has conjectured that every generalized triangle group G satisfies the Tits alternative. It is known that the conjecture holds except possibly when the triple (p, q, r) is one of (2, 3, 2), (2, 4, 2), (2, 5, 2), (3, 3, 2), (3, 4, 2), or (3, 5, 2). Building on a result of Benyash-Krivets and Barkovich from this journal, we show that the Tits alternative holds in the case (p, q, r) = (3, 4, 2).

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 04 Jan 2012 12:26
Last Modified: 18 Oct 2017 16:18
URI: http://repository.essex.ac.uk/id/eprint/1798

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