# arithmetic fuchsian group in a sentence

- and a similar bound holds for more general
*arithmetic Fuchsian groups*. - A similar bound holds for more general
*arithmetic Fuchsian groups*. - A natural question is to identify those among
*arithmetic Fuchsian groups* which are not strictly contained in a larger discrete subgroup. - 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*. - 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. - It's difficult to find
*arithmetic fuchsian group* in a sentence. *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 ).- 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. - 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 ).