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

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

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

## 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 |
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Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematical Sciences, Department of |

SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |

Depositing User: | Unnamed user with email elements@essex.ac.uk |

Date Deposited: | 04 Jan 2012 12:26 |

Last Modified: | 06 Jan 2022 13:27 |

URI: | http://repository.essex.ac.uk/id/eprint/1798 |

## Available files

**Filename:** GeneralizedTriangleGps342.pdf