Metric approximations of unrestricted wreath products when the acting group is amenable
Group Theory
2022-02-17 v4
Abstract
We give a simple and unified proof showing that the unrestricted wreath product of a weakly sofic, sofic, linear sofic, or hyperlinear group by an amenable group is weakly sofic, sofic, linear sofic, or hyperlinear, respectively. By means of the Kaloujnine-Krasner theorem, this implies that group extensions with amenable quotients preserve the four aforementioned metric approximation properties. We also discuss the case of co-amenable groups.
Keywords
Cite
@article{arxiv.2004.05735,
title = {Metric approximations of unrestricted wreath products when the acting group is amenable},
author = {Javier Brude and Román Sasyk},
journal= {arXiv preprint arXiv:2004.05735},
year = {2022}
}
Comments
v4: Final version. To appear in Communications in Algebra. A new section was added, which deals with the case when a group has a co-amenable subgroup that is weakly sofic, sofic, linear sofic, or hyperlinear, respectively. 13 pages