Abels's groups revisited

Abstract

We generalize a class of groups introduced by Herbert Abels to produce examples of virtually torsion free groups that have Bredon-finiteness length $m-1$ and classical finiteness length $n-1$ for all $0<m\le n$.

The proof illustrates how Bredon-finiteness properties can be verified using geometric methods and a version of Brown’s criterion due to Martin Fluch and the author.