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

Howie, James, Williams, Gerald (2006) Free subgroups in certain generalized triangle groups of type (2, m, 2). Geometriae Dedicata, 119 (1). pp. 181-197. ISSN 0046-5755. (doi:10.1007/s10711-006-9068-x) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:10473)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL:
http://dx.doi.org/10.1007/s10711-006-9068-x

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
DOI/Identification number: 10.1007/s10711-006-9068-x
Uncontrolled keywords: generalised triangle group; free subgroup; Tits alternative
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 05 Sep 2008 22:26 UTC
Last Modified: 16 Nov 2021 09:49 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/10473 (The current URI for this page, for reference purposes)

University of Kent Author Information

Williams, Gerald.

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