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# 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. (doi:10.1515/JGT.2007.009) (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)

 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. (Contact us about this Publication) Official URLhttp://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 10.1515/JGT.2007.009 FREE-PRODUCTS; RELATOR; CYCLICS Q Science > QA Mathematics (inc Computing science) Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Judith Broom 07 Jul 2008 10:03 UTC 28 May 2019 13:47 UTC https://kar.kent.ac.uk/id/eprint/10476 (The current URI for this page, for reference purposes)
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