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2008 Derived Arithmetic Fuchsian Groups of Genus Two
Melissa L. Macasieb
Experiment. Math. 17(3): 347-369 (2008).


We classify all cocompact torsion-free derived arithmetic Fuchsian groups of genus two by commensurability class. In particular, we show that there exist no such groups arising from quaternion algebras over number fields of degree greater than 5. We also prove some results on the existence and form of maximal orders for a class of quaternion algebras related to these groups. Using these results in conjunction with a computer program, one can determine an explicit set of generators for each derived arithmetic Fuchsian group containing a torsionfree subgroup of genus two. We show this for a number of examples.


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Melissa L. Macasieb. "Derived Arithmetic Fuchsian Groups of Genus Two." Experiment. Math. 17 (3) 347 - 369, 2008.


Published: 2008
First available in Project Euclid: 19 November 2008

zbMATH: 1184.11015
MathSciNet: MR2455706

Primary: 11R52 , 57M50

Keywords: arithmetic fuchsian groups , Hyperbolic orbifolds , maximal orders

Rights: Copyright © 2008 A K Peters, Ltd.


Vol.17 • No. 3 • 2008
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