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