- Title
- Quantifying conjugacy separability in wreath products of groups
- Creator
- Ferov, Michal; Pengitore, Mark
- Relation
- Quarterly Journal of Mathematics Vol. 73, Issue 4, p. 1555-1593
- Publisher Link
- http://dx.doi.org/10.1093/qmath/haac031
- Publisher
- Oxford University Press
- Resource Type
- journal article
- Date
- 2022
- Description
- We study generalizations of conjugacy separability in restricted wreath products of groups. We provide an effective upper bound for C-conjugacy separability of a wreath product A≀B in terms of the C-conjugacy separability of A and B, the growth of C-cyclic subgroup separability of B and the C-residual girth of B. As an application, we provide a characterization of when A≀B is p-conjugacy separable. We use this characterization to provide for each prime p an example of a wreath product with infinite base group that is p-conjugacy separable. We also provide asymptotic upper bounds for conjugacy separability for wreath products of nilpotent groups, which include the lamplighter groups and provide asymptotic upper bounds for conjugacy separability of the free metabelian groups.
- Subject
- wreath products; conjugacy separability; groups; characterization
- Identifier
- http://hdl.handle.net/1959.13/1487849
- Identifier
- uon:52265
- Identifier
- ISSN:0033-5606
- Rights
- © The Author(s) 2022. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
- Language
- eng
- Full Text
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