A cancellation theorem for metacyclic group rings

A ring has stably free cancellation when every stably free -module is free. Let G = Cp Cq be a finite metacyclic group where p is an odd prime and q is a positive integral divisor of p - 1. We show that the group ring R[G] has stably free cancellation when is a ring of mixed polynomials and Laurent polynomials over the integers. As a consequence, when C (m) 8 is the free abelian group of rank m then the integral group ring Z[G( p, q) x C (m) 8] has stably free cancellation.