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

SASYK, ROMÁN; BRUDE, JAVIER

COMMUNICATIONS IN ALGEBRA

TAYLOR & FRANCIS INC

Año: 2021 vol. 50 p. 1 - 13

0092-7872

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.