Williams, Gerald
(2007)
*
Pseudo-elementary generalized triangle groups.
*
Journal of Group Theory,
10
(1).
pp. 101-115.
ISSN 1433-5883.
(doi:https://doi.org/10.1515/JGT.2007.009)
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Official URL http://dx.doi.org/10.1515/JGT.2007.009 |

## Abstract

A generalized triangle group is a group that can be presented in the form Gamma = [x, y\x(l) = y(m) = w(x, y)(n) = 1] where l, m, n is an element of {2,3,4....} boolean OR {infinity} and w(x, y) is an element of the free product [x, y\ x(l) = y(m) = 1] involving both x and y. A homomorphism phi : Gamma --> G is said to be essential if phi(x), phi(y), phi(w(x, y)) have orders l, m, n respectively. Every generalized triangle group Gamma admits an essential representation to PSL(2, C). In most cases there will be such a representation with infinite or non-elementary image. Vinberg and Kaplinsky say that Gamma is pseudo-finite if the image of any essential representation Gamma --> PSL(2, C) is finite and they have obtained a partial classification of such groups. Extending this concept, we call F pseudo-elementary if the image of any essential representation Gamma --> PSL(2, C) is elementary. In this paper we classify the pseudo-elementary generalized triangle groups F with n >= 3 and obtain partial results in the case n = 2.

Item Type: | Article |
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Uncontrolled keywords: | FREE-PRODUCTS; RELATOR; CYCLICS |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics |

Depositing User: | Judith Broom |

Date Deposited: | 07 Jul 2008 10:03 UTC |

Last Modified: | 14 Jan 2010 14:40 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/10476 (The current URI for this page, for reference purposes) |

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