Pseudo-elementary generalized triangle groups

Williams, Gerald (2007) Pseudo-elementary generalized triangle groups. Journal of Group Theory, 10 (1). pp. 101-115. ISSN 1433-5883. (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)

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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
Uncontrolled keywords: FREE-PRODUCTS; RELATOR; CYCLICS
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: 07 Jul 2008 10:03
Last Modified: 14 Jan 2010 14:40
Resource URI: https://kar.kent.ac.uk/id/eprint/10476 (The current URI for this page, for reference purposes)
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