This question is, essentially, a comment of Mark Sapir. I think it deserves to be a question. A countable, discrete group $\Gamma$ is $sofic$ if for every $\epsilon>0$ and finite …

Let $K$ be a finite field and $G$ be a discrete group. Is it true that for every $a=e+a_1+\ldots+a_n,b=e+b_1+\ldots+b_m\in K[G]$ with $b_i\neq e,a_j\neq e$ the condition $ab= …

A discrete group $\Gamma$ has zipper action if there is a set $X$ and an action of $\Gamma$ on $X$ (say left-action) and a subset $Z\subseteq X$ such that for every $g \in \Gamm …