Elementary Action of Classical Groups on Unimodular Rows Over Monoid Rings

Abstract

The elementary action of symplectic and orthogonal groups on unimodular rows of length 2n is transitive for 2n >= max(4,d+2) in the symplectic case, and 2n >= max(6,2d+4) in the orthogonal case, over monoid rings R[M], where R is a commutative noetherian ring of dimension d, and M is commutative cancellative torsion free monoid. As a consequence, one gets the surjective stabilization bound for the K-1 for classical groups. This is an extension of J. Gubeladze's results for linear groups