Stably free cancellation for group rings of metacyclic type

摘要

Let $p,q$ be primes such that $q,|,p- 1$. Write $F_{n}$ for the free group of rank $ngeq 1$ and let $G(p,q)=C_{p}times C_{q}$. We show that any stably free module over $mathbb{Z}[G(p,q)imes F_{n}]$ is necessarily free.