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GENERATING SYSTEMS OF SUBGROUPS IN PSL(2,Γn)

Published online by Cambridge University Press:  05 February 2002

Xiantao Wang  and
Weiqi Yang
Xiantao Wang
Affiliation:
Department of Applied Mathematics, Hunan University, Changsha, Hunan 410082, People's Republic of China ([email protected])
Weiqi Yang
Affiliation:
Department of Applied Mathematics, Beijing Institute of Technology, PO Box 327, Beijing 100081, People's Republic of China
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Abstract

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It is proved in this paper that for any non-elementary subgroup $G$ of $\mathrm{PSL}(2,\sGa_n)$, which has no elliptic element, to be not strict, there is a minimal generating system of $G$ consisting of loxodromic elements, and that if $G$ is a non-elementary subgroup of $\mathrm{PSL}(2,\sGa_n)$ of which each loxodromic element is hyperbolic, then $G$ is conjugate to a subgroup of $\mathrm{PSL}(2,\mathbb{R})$.

AMS 2000 Mathematics subject classification: Primary 30F40. Secondary 20H10

Keywords

Möbius transformationClifford algebragenerating system
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 1 , February 2002 , pp. 49 - 58
Copyright
Copyright © Edinburgh Mathematical Society 2002