Bounded generation of S-arithmetic subgroups of isotropic orthogonal groups over number fields

Igor V. Erovenko; Andrei S. Rapinchuk

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Bounded generation of S-arithmetic subgroups of isotropic orthogonal groups over number fields

Igor V. Erovenko·Andrei S. Rapinchuk

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Abstract

Let f be a nondegenerate quadratic form in at least 5 variables over a number field K and let S be a finite set of valuations of K containing all Archimedean ones. We prove that if the Witt index of f is at least 2 or it is 1 and S contains a non-Archimedean valuation, then the S-arithmetic subgroups of the special orthogonal group of f have bounded generation. These groups provide a series of examples of boundedly generated S-arithmetic groups in isotropic, but not quasi-split, algebraic groups.

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BibTeX RIS

Igor V. Erovenko, Andrei S. Rapinchuk. 2005-08-29. Bounded generation of S-arithmetic subgroups of isotropic orthogonal groups over number fields. https://arxiv.org/abs/math/0508480

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