Residual Finiteness Growths of Virtually Special Groups
  Let $G$ be a virtually special group. Then the residual finiteness growth of $G$ is at most linear. This result cannot be found by embedding $G$ into a special linear group. Indeed, the special linear group $\text{SL}_k(\mathbb{Z})$, for $k > 2$, has residual finiteness growth $n^{k-1}$. 
Khalid Bou-Rabee, Mark F. Hagen, Priyam Patel
math.GR math.GT