Groups with infinite virtual cohomological dimension which act freely on \(\mathbb{R}{}^ m\times{} S^{n-1}\) (Q1183360)

\textit{F. X. Connolly} and \textit{S. Prassidis} proved [Topology 28, No. 2, 133-148 (1989; Zbl 0703.57025)] that a countable group with finite virtual cohomological dimension (vcd) acts freely and properly discontinuously on \(\mathbf{R}^ m\times S^{n-1}\) if and only if it has periodic Farrell cohomology. The paper under review extends the methods and some of the results of the former to those countable groups with infinite vcd for which the Farrell cohomology can be defined. In particular, the author constructs free and properly discontinuous actions on \(\mathbf{R}^ m\times S^{n-1}\) for certain countable groups with infinite vcd and periodic Farrell cohomology. Among those groups are the locally cyclic and the locally quaternionic groups.