Bounded generation of S-arithmetic subgroups of isotropic orthogonal groups over number fields
Group Theory
2007-05-23 v2
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.
Cite
@article{arxiv.math/0508480,
title = {Bounded generation of S-arithmetic subgroups of isotropic orthogonal groups over number fields},
author = {Igor V. Erovenko and Andrei S. Rapinchuk},
journal= {arXiv preprint arXiv:math/0508480},
year = {2007}
}
Comments
An extended version of the paper accepted by the Journal of Number Theory, it includes a self-contained proof of Witt's theorem for local lattices