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

Howie, J. and Williams, G. (2006) Free subgroups in certain generalized triangle groups of type (2, m, 2). Geometriae Dedicata, 119 (1). pp. 181-197. ISSN 0046-5755 . (The full text of this publication is not available from this repository)

The full text of this publication is not available from this repository. (Contact us about this Publication)
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
Uncontrolled keywords: generalised triangle group; free subgroup; Tits alternative
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Judith Broom
Date Deposited: 05 Sep 2008 22:26
Last Modified: 14 Jan 2010 14:40
Resource URI: http://kar.kent.ac.uk/id/eprint/10473 (The current URI for this page, for reference purposes)
  • Depositors only (login required):