Cohomological dimension of soluble groups
This paper turns a conjecture of Gildenhuys and Strebel into the following Theorem. Let G be a soluble group. Then the following are equivalent: (i) \(cd_{{\mathbb{Z}}}G=hd_{{\mathbb{Z}}}G<\infty\). (ii) G is of type FP. (iii) G is a duality group. (iv) G is torsion-free and constructible. The proof is based on an important reduction due to Gildenhuys and Strebel. Their result allows to restrict attention to a special kind of metabelian groups. The skillful combination of homological tools with elementary commutative algebra and point set topology is reminiscent of earlier work by the same author.
scientific article; zbMATH DE number 3973157