Residual Finiteness Growths of Virtually Special Groups

Abstract

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 $n^{k-1}$.

Updated version contains minor changes incorporating referee comments/suggestions and a simplified proof of Lemma 4.1

References in corpus (3)

• Virtual cubulation of nonpositively curved graph manifolds
• A metric Kan-Thurston theorem
• Quantifying residual finiteness of arithmetic groups

Cited by in corpus (1)

• Residual Finiteness Growth in Virtually Abelian Groups