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

โœ Scribed by Igor V. Erovenko; Andrei S. Rapinchuk

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
208 KB
Volume
119
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

Let f be a nondegenerate quadratic form in n 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 2 or it is 1 and S contains a non-Archimedean valuation, then the S-arithmetic subgroups of SO n (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.

๐Ÿ“œ SIMILAR VOLUMES

Two-Element Generation of Orthogonal Gro
Two-Element Generation of Orthogonal Groups over Finite Fields
โœ H. Ishibashi; A.G. Earnest ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 294 KB

Minimal sets of generators of the orthogonal groups on nonsingular quadratic spaces over a finite field are studied. All such orthogonal groups are shown to be generated by two elements, with the possible exception of two low-dimensional cases. 1994 Academic Press, Inc.