21.86 (2026)

(M. Gromov, B.Weiss). A group $G$ is said to be sofic if for every finite set $F \subseteq G$ containing 1 and every $\varepsilon > 0$ there exist $n \in \mathbb{N}$ and a map $\phi : F \to S_n$ such that $\phi(1) = 1$, $d(\phi(gh), \phi(g)\phi(h)) < \varepsilon$ for all $g, h$ such that $gh \in F$, $\phi(g)$ does not have fixed points for every $g \in F \setminus \{1\}$.

Is every group sofic?