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# arithmetic fuchsian group in a sentence

1. and a similar bound holds for more general arithmetic Fuchsian groups.
2. A similar bound holds for more general arithmetic Fuchsian groups.
3. A natural question is to identify those among arithmetic Fuchsian groups which are not strictly contained in a larger discrete subgroup.
4. Any order in a quaternion algebra over \ mathbb Q which is not split over \ mathbb Q but splits over \ mathbb R yields a cocompact arithmetic Fuchsian group.
5. An arithmetic Fuchsian group is constructed from the following data : a totally real number field F, a quaternion algebra A over F and an order \ mathcal O in A.
6. It's difficult to find arithmetic fuchsian group in a sentence.
7. Arithmetic Fuchsian groups can be constructed directly in the latter group by taking the integral points in the orthogonal group associated to quadratic forms defined over number fields ( and satisfying certain conditions ).
8. If \ Gamma is an arithmetic Fuchsian group then k \ Gamma and A \ Gamma together are a number field and quaternion algebra from which a group commensurable to \ Gamma may be derived.
9. The simplest example of an arithmetic Fuchsian group is the modular \ mathrm { PSL } _ 2 ( \ mathbb Z ), which is obtained by the construction above with A = M _ 2 ( \ mathbb Q ) and \ mathcal O = M _ 2 ( \ mathbb Z ).

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