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arXiv · 1309.7993

Intersection growth in groups

Ian Biringer·Khalid Bou-Rabee·Martin Kassabov·Francesco Matucci
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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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Ian Biringer, Khalid Bou-Rabee, Martin Kassabov, Francesco Matucci. 2013-12-04. Intersection growth in groups. https://arxiv.org/abs/1309.7993

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