Commensurators and classifying spaces with virtually cyclic stabilizers

2011/08/31 by Dieter Degrijse, Degrijse, Dieter, Nansen Petrosyan +1
Mathematics · #20F65 #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GR #msc:20F65

paper · pdf · doi:10.48550/arxiv.1108.6279

12 pages

arxiv created 2011/08/31 · openalex publication_date 2011/08/31 · arxiv updated 2011/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Geometric dimension of groups for the family of virtually cyclic subgroups
• On the classifying space for the family of virtually cyclic subgroups for elementary amenable groups
• On the finiteness of the classifying space for the family of virtually cyclic subgroups
• Classifying Spaces with Virtually Cyclic Stabilisers for Certain Infinite Cyclic Extensions
• On the classifying space of the family of virtually cyclic subgroups