Michal Ferov ; Mark Pengitore - Bounding conjugacy depth functions for wreath products of finitely generated abelian groups

gcc:11728 - journal of Groups, complexity, cryptology, September 28, 2023, Volume 15, Issue 1 - https://doi.org/10.46298/jgcc.2023.15.1.11728
Bounding conjugacy depth functions for wreath products of finitely generated abelian groupsArticle

Authors: Michal Ferov ; Mark Pengitore

    In this article, we study the asymptotic behaviour of conjugacy separability for wreath products of abelian groups. We fully characterise the asymptotic class in the case of lamplighter groups and give exponential upper and lower bounds for generalised lamplighter groups. In the case where the base group is infinite, we give superexponential lower and upper bounds. We apply our results to obtain lower bounds for conjugacy depth functions of various wreath products of groups where the acting group is not abelian.


    Volume: Volume 15, Issue 1
    Published on: September 28, 2023
    Accepted on: September 15, 2023
    Submitted on: August 15, 2023
    Keywords: Mathematics - Group Theory
    Funding:
      Source : OpenAIRE Graph
    • Geometry, Topology, and Dynamics of Spaces of Non-Positive Curvature; Funder: National Science Foundation; Code: 1812028
    • Australian Laureate Fellowships - Grant ID: FL170100032; Funder: Australian Research Council (ARC); Code: FL170100032

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