Generalized triangle groups
Published online by Cambridge University Press: 24 October 2008
Extract
A group G is called a triangle group if it can be presented in the form
It is well-known that G is isomorphic to a subgroup of PSL2(ℂ), that a is of order l, b is of order m and ab is of order n. If
then G contains the fundamental group of a positive genus orientable surface as a subgroup of finite index whenever s(G) ≤ 1; in particular G is infinite. Furthermore, if s(G) < 1, the genus of the surface is greater than 1 and consequently G contains a free group of rank 2.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 1 , July 1987 , pp. 25 - 31
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- Copyright © Cambridge Philosophical Society 1987
References
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