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By examining commensurators of virtually cyclic groups, we show that for eachnatural number n, any locally finite-by-virtually cyclic group of cardinalityaleph_n admits a finite dimensional classifying space with virtually cyclicstabilizers of dimension n+3. As a corollary, we prove that every elementaryamenable group of finite Hirsch length and cardinality aleph_n admits a finitedimensional classifying space with virtually cyclic stabilizers.

Commensurators and classifying spaces with virtually cyclic stabilizers