Intersection growth in groups

Biringer, Ian; Bou-Rabee, Khalid; Kassabov, Martin; Matucci, Francesco

doi:10.1090/tran/6865

Intersection growth in groups
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by Ian Biringer, Khalid Bou-Rabee, Martin Kassabov and Francesco Matucci PDF

Trans. Amer. Math. Soc. 369 (2017), 8343-8367 Request permission

Abstract:

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.

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