Intersection growth in groups
Biringer, Ian; Bou-Rabee, Khalid; Kassabov, Martin; Matucci, Francesco
To appear in Transactions of the American Mathematical Society
The intersection growth of a group $G$ is the asymptotic behavior of the index of the intersection of all subgroups of $G$ with index at most $n$, and measures the Hausdorff dimension of $G$ in profinite metrics. We study intersection growth in free groups and special linear groups and relate intersection growth to quantifying residual finiteness.