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 <= 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.

17 pages, 2 figures, v2 more detailed

References in corpus (3)

• Brown's criterion in Bredon homology
• Spherical subcomplexes of spherical buildings
• Centralisers of Finite Subgroups in Soluble Groups of Type FP_n

Cited by in corpus (1)

• On the finiteness length of some soluble linear groups