2005/04/28 by G. Bell, Gregory C. Bell, Bell, Gregory C. · 1 citation
Mathematics · #20E22 #20F65 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Holomorphic and Operator Theory #Primary: 20F69 #Secondary 20E06 #math.GR #msc:20E06 #msc:20E22 #msc:20F65 #msc:20F69
paper · pdf · doi:10.48550/arxiv.math/0504577
14 pages, no figures
arxiv created 2005/04/28 · openalex publication_date 2005/04/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is relatively easy to construct a finitely generated group with infinite asymptotic dimension: the restricted wreath product of ℤ by ℤ provides an example. In light of this, it becomes interesting to consider the rate of growth of the asymptotic dimension function of a group. Loosely speaking, we measure the dimension on λ-scale and let λ increase to infinity to recover the asymptotic dimension. In this paper we consider how the asymptotic dimension function is affected by different constructions involving groups.