Logarithmic bounds for the diameters of some Cayley graphs

Lam Pham, Xin Zhang

Let $S\subset {\text{GL}}_n(\mathbb{Z})$ be a finite symmetric set. We show that if the Zariski closure of $\Gamma =⟨S⟩$ is a product of ${\text{SL}}_d$ or a special affine linear…