Williams, G (2007) Pseudo-elementary Generalized Triangle Groups. Journal of Group Theory, 10 (1). pp. 101-115. DOI https://doi.org/10.1515/jgt.2007.009
Williams, G (2007) Pseudo-elementary Generalized Triangle Groups. Journal of Group Theory, 10 (1). pp. 101-115. DOI https://doi.org/10.1515/jgt.2007.009
Williams, G (2007) Pseudo-elementary Generalized Triangle Groups. Journal of Group Theory, 10 (1). pp. 101-115. DOI https://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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Subjects: | Q Science > QA Mathematics |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 25 May 2012 09:25 |
Last Modified: | 16 May 2024 18:30 |
URI: | http://repository.essex.ac.uk/id/eprint/2403 |
Available files
Filename: jgt.2007.009.pdf