Howie, James and 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 .
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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 |
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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: | 25 Jun 2014 13:08 |

Resource URI: | https://kar.kent.ac.uk/id/eprint/10473 (The current URI for this page, for reference purposes) |

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