The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Groups, Geometry, and Dynamics


Full-Text PDF (173 KB) | Metadata | Table of Contents | GGD summary
Volume 7, Issue 3, 2013, pp. 543–555
DOI: 10.4171/GGD/196

Published online: 2013-08-27

Commensurators and classifying spaces with virtually cyclic stabilizers

Dieter Degrijse[1] and Nansen Petrosyan[2]

(1) University of Copenhagen, Denmark
(2) University of Southampton, UK

By examining commensurators of virtually cyclic groups, we show that for each natural number $n$, any locally finite-by-virtually cyclic group of cardinality $\aleph_n$ admits a finite dimensional classifying space with virtually cyclic stabilizers of dimension $n+3$. As a corollary, we prove that every elementary amenable group of finite Hirsch length and cardinality $\aleph_n$ admits a finite dimensional classifying space with virtually cyclic stabilizers.

Keywords: Commensurator, classifying space, elementary amenable group

Degrijse Dieter, Petrosyan Nansen: Commensurators and classifying spaces with virtually cyclic stabilizers. Groups Geom. Dyn. 7 (2013), 543-555. doi: 10.4171/GGD/196