Super approximation for ${\text{SL}}_2\times {\text{SL}}_2$ and ${\text{ASL}}_2$

Jincheng Tang, Xin Zhang

Let $S\subset {\text{SL}}_2(\mathbb{Z})\times {\text{SL}}_2(\mathbb{Z})$ or ${\text{SL}}_2(\mathbb{Z})⋉{\mathbb{Z}}^2$ be finite symmetric and assume $S$ generates a group $G$ which is…