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arXiv · 2004.05735

Metric approximations of unrestricted wreath products when the acting group is amenable

Javier Brude·Román Sasyk
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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.

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BibTeXRIS

Javier Brude, Román Sasyk. 2020-04-13. Metric approximations of unrestricted wreath products when the acting group is amenable. https://doi.org/10.1080/00927872.2021.1976790

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