Bounded generation of SL(n,A) (after D. Carter, G. Keller and E. Paige)
Abstract
We present unpublished work of D.Carter, G.Keller, and E.Paige on bounded generation in special linear groups. Let n be a positive integer, and let A = O be the ring of integers of an algebraic number field K (or, more generally, let A be a localization O_S.) If n = 2, assume that A has infinitely many units. We show there is a finite-index subgroup H of SL(n,A), such that every matrix in H is a product of a bounded number of elementary matrices. We also show that if T is in SL(n,A), and T is not a scalar matrix, then there is a finite-index, normal subgroup N of SL(n,A), such that every element of N is a product of a bounded number of conjugates of T. For n > 2, these results remain valid when SL(n,A) is replaced by any of its subgroups of finite index.
Keywords
Cite
@article{arxiv.math/0503083,
title = {Bounded generation of SL(n,A) (after D. Carter, G. Keller and E. Paige)},
author = {Dave Witte Morris},
journal= {arXiv preprint arXiv:math/0503083},
year = {2007}
}
Comments
44 pages, no figures. Many minor errors corrected