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Journal of the London Mathematical Society 2006 73(1):14-30; doi:10.1112/S0024610705022428
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© The London Mathematical Society

Torsion in Arithmetic Fuchsian Groups

C. Maclachlan

Department of Mathematical Sciences, University of Aberdeen Aberdeen AB24 3UE, United Kingdom C.Maclachlan{at}maths.abdn.ac.uk

Received 10 May 2004. Revision received 24 November 2004.

In this paper a formula is derived for the number of conjugacy classes of cyclic subgroups of finite order in those arithmetic Fuchsian groups which are of minimal covolume in their commensurability class. The formula is entirely in terms of the number theoretic data defining the commensurability class of the arithmetic group so that, in particular, any two such groups of minimal covolume in the class, will be isomorphic.


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