Inducing Super-Approximation

Alireza Salehi Golsefidy, Xin Zhang

Let ${\Gamma }_2\subseteq {\Gamma }_1$ be finitely generated subgroups of ${\mathrm{GL}}_{n_0}(\mathbb{Z}[1/q_0])$. For $i=1$ or $2$, let ${\mathbb{G}}_i$ be the Zariski-closure of ${\Gamma }_i$ in $({\rm GL}_{n…