Commensurators and classifying spaces with virtually cyclic stabilizers

Abstract

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.

12 pages

References in corpus (1)

• Classifying spaces for proper actions of locally-finite groups

Cited by in corpus (1)

• On the classifying space for the family of virtually cyclic subgroups for elementary amenable groups