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.
Biringer, I., Bou-Rabee, K., Kassabov, M., Matucci, F. (2017). Intersection growth in groups. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 369(12), 8343-8367 [10.1090/tran/6865].
Intersection growth in groups
Matucci, Francesco
Co-primo
2017
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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