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Bounded generation of SL(n, A) (After D. Carter, G. Keller, and E. Paige)

By Dave Witte Morris

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We present unpublished work of D. Carter, G. Keller, and E. Paige on bounded generation in special linear groups.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 OS −1). 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 ∈ 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 ≥ 3, these results remain valid when SL(n, A) is replaced by any o

Topics: Contents
Year: 2007
OAI identifier: oai:CiteSeerX.psu:10.1.1.161.7925
Provided by: CiteSeerX
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