Intersection growth in groups
Group Theory
2013-12-06 v2
Abstract
The intersection growth of a group is the asymptotic behavior of the index of the intersection of all subgroups of with index at most , and measures the Hausdorff dimension of in profinite metrics. We study intersection growth in free groups and special linear groups and relate intersection growth to quantifying residual finiteness.
Cite
@article{arxiv.1309.7993,
title = {Intersection growth in groups},
author = {Ian Biringer and Khalid Bou-Rabee and Martin Kassabov and Francesco Matucci},
journal= {arXiv preprint arXiv:1309.7993},
year = {2013}
}
Comments
20 pages, no figures. Revised version. We extend estimates to polycyclic groups and explain why normal intersection growth is a profinite invariant. Theorem 6.1 previously contained an error which has now been fixed