JournalsggdVol. 7, No. 3pp. 543–555

Commensurators and classifying spaces with virtually cyclic stabilizers

  • Dieter Degrijse

    University of Copenhagen, Denmark
  • Nansen Petrosyan

    University of Southampton, UK
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Abstract

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

Cite this article

Dieter Degrijse, Nansen Petrosyan, Commensurators and classifying spaces with virtually cyclic stabilizers. Groups Geom. Dyn. 7 (2013), no. 3, pp. 543–555

DOI 10.4171/GGD/196