  In the paper, we develop further the properties of Schur rings over infinite
groups, with particular emphasis on the virtually cyclic group $\Z\times\Z_p$,
where $p$ is a prime. We provide structure theorems for primitive sets in these
Schur rings. In the case of Fermat and safe primes, a complete classification
theorem is proven, which states that all Schur rings over $\Z\times\Z_p$ are
traditional. We also draw analogs between Schur rings over $\Z\times\Z_p$ and
partitions of difference sets over $\Z_p$.
