Asymptotic Property C for Certain Wreath-like Products of Groups

2025/05/02 by Liu, Han
Mathematics · #20F69 #51F30 #54F45 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2505.01268

openalex publication_date 2025/05/02 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

In this paper, we present generalizations of some results on the asymptotic property C for wreath products. Specifically, we prove that certain wreath-like products admit asymptotic property C, thus providing some new examples for further study.

Citations

• Wreath-like products of groups and their von Neumann algebras I: W^∗-superrigidity
• Decomposition theorems for asymptotic property C and property A
• Classification of metric spaces with infinite asymptotic dimension
• Tilings of amenable groups
• A notion of geometric complexity and its application to topological rigidity
• Asymptotic Dimension
• Some notes on property A
• Asymptotic Dimension of Discrete Groups
• On transfinite extension of asymptotic dimension
• Asymptotic dimension in Bedlewo
• Asymptotic dimension of relatively hyperbolic groups
• A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory
• Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits)

Related

• Asymptotic property C of the wreath product ZwrZ
• On asymptotic property C
• Growth of the asymptotic dimension function for groups
• Growth of groups and wreath products
• Wreath product of groups with infinite conjugacy classes