Abstract.
A group is of type VF if it has a finite-index subgroup which has a finite classifying space. We construct groups of type VF in which the centralizers of some elements of finite order are not of type VF and groups of type VF containing infinitely many conjugacy classes of finite subgroups. It follows that a group G of type VF need not admit a finite-type universal proper G-space. We construct groups G for which the minimal dimension of a universal proper G-space is strictly greater than the virtual cohomological dimension of G. Each of our groups embeds in GL m (ℤ) for sufficiently large m. Some applications to K-theory are also considered.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Oblatum 26-IV-2001 & 3-VII-2002¶Published online: 10 October 2002
Rights and permissions
About this article
Cite this article
Leary, I., Nucinkis, B. Some groups of type VF. Invent. math. 151, 135–165 (2003). https://doi.org/10.1007/s00222-002-0254-7
Issue Date:
DOI: https://doi.org/10.1007/s00222-002-0254-7