Bounded Generation of S-Arithmetic Subgroups of Isotropic Orthogonal Groups over Number Fields

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Igor Erovenko, Associate Professor and Director of Undergraduate Study (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/

Abstract: Let f be a nondegenerate quadratic form in n ¾ 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 ¾ 2 or it is 1 and S contains a non- Archimedean valuation, then the S-arithmetic subgroups of SOn( f ) have bounded generation. These groups provide a series of examples of boundedly generated Sarithmetic groups in isotropic, but not quasi-split, algebraic groups.

Additional Information

Publication
Journal of Number Theory (2006): 119.1, 28-48
Language: English
Date: 2006

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