Euler characteristics and cohomology of \(p\)-local discrete groups (Q1188279)

The author formulates a local approach for the cohomological analysis of a discrete group of finite virtual cohomological dimension. An essential aspect is the use of Farrell Cohomology. One of the main points is that the mod-p cohomology not only depends on the finite p-subgroups but also on p-subgroups of finite quotient groups. One result is a cohomological non-vanishing theorem which relates rational cohomology and mod-p cohomology in the case of such a group with p-torsion but has a normal torsion-free subgroup of p-power index. For example, a semi-direct product of a torsion-free group by a finite p-group.