Bounded generation of SL(n,A) (after D. Carter, G. Keller and E. Paige)
| dc.creator | Morris, Dave Witte | |
| dc.date | 2005-03-05 | |
| dc.date | 2007-09-17 | |
| dc.date.accessioned | 2026-07-07T08:32:41Z | |
| dc.date.available | 2026-07-07T08:32:41Z | |
| dc.description | We present unpublished work of D.Carter, G.Keller, and E.Paige on bounded generation in special linear groups.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. | |
| dc.description | 44 pages, no figures. Many minor errors corrected | |
| dc.identifier | https://arxiv.org/abs/math/0503083 | |
| dc.identifier | http://arxiv.org/abs/math/0503083 | |
| dc.identifier | New York Journal of Mathematics 13 (2007) 383-421; http://nyjm.albany.edu/j/2007/13-17.html | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138870 | |
| dc.subject | Group Theory | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Number Theory | |
| dc.subject | 20H05 (Primary); 11F06, 19B37 (Secondary) | |
| dc.title | Bounded generation of SL(n,A) (after D. Carter, G. Keller and E. Paige) | |
| dc.type | text |