Discrete groups with large exponents in cohomology

Abstract

Let Γ be a discrete group of finite virtual cohomological dimension. The Farrell cohomology of Γ,Ĥ ∗( Γ, Z ), depends on the finite subgroups of Γ, in a manner which is not yet well-understood. In this paper we produce examples of groups with nontrivial finite subgroups of order at most p (a prime) but with arbitrarily high p-torsion in their Farrell cohomology. We describe a method for constructing discrete groups with large exponents starting from a finite group acting freely on an aspherical complex.