Bounding conjugacy depth functions for wreath products of finitely generated abelian groups

Abstract

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.

33 pages. Published in journal of Groups, Complexity, Cryptology. arXiv admin note: substantial text overlap with arXiv:2111.14722

References in corpus (4)

• On conjugacy separability of graph products of groups
• Decision problems, complexity, traces, and representations
• Separating cyclic subgroups in graph products of groups
• Quantifying conjugacy separability in wreath products of groups