Groups, Geometry, and Dynamics


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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