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

By Dave Witte Morris. 2005

67 citations recorded by the source corpus.

We present unpublished work of D.Carter, G.Keller, and E.Paige on bounded generation in special linear groups.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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bde48a9089f7d4b5377826ede60482919145a801