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Free subgroups in certain generalized triangle groups of type (2,m,2)

Williams, G and Howie, J (2006) 'Free subgroups in certain generalized triangle groups of type (2,m,2).' Geometria Dedicata, 119 (1). pp. 181-197. ISSN 0046-5755

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Abstract

A generalized triangle group is a group that can be presented in the form G = < x, y vertical bar x(p) = y(q) = w( x, y)(r) = 1 > where p, q, r >= 2 and w(x, y) is a cyclically reduced word of length at least 2 in the free product Z(p)*Z(q) = < x, y vertical bar x(p) = y(q) = 1 >. 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 (3, 3, 2), (3, 4, 2), (3, 5, 2), or (2, m, 2) where m = 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. In this paper, we show that the Tits alternative holds in the cases ( p, q, r) = ( 2, m, 2) where m = 6, 10, 12, 15, 20, 30, 60.

Item Type: Article
Uncontrolled Keywords: generalised triangle group; free subgroup; 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 09:31
Last Modified: 06 Jan 2022 13:27
URI: http://repository.essex.ac.uk/id/eprint/2404

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