Extensions of a residually finite group by a weakly sofic group are weakly sofic

Abstract

In this paper, we show that residually-finite-by-weakly-sofic extensions are weakly sofic. More precisely, we show that if in an exact sequence of groups $1\to N\hookrightarrow K\twoheadrightarrow G\to 1$ the group $G$ is residually finite and $N$ is weakly sofic, then $K$ is weakly sofic.