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.References
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Additional Information
- Ian Biringer
- Affiliation: Department of Mathematics, Carney Hall, Boston College, Chestnut Hill, Massachusetts 02467-3806
- Email: ian.biringer@bc.edu
- Khalid Bou-Rabee
- Affiliation: Department of Mathematics, 2074 East Hall, University of Michigan, Ann Arbor, Michigan 48109-1043
- Address at time of publication: Department of Mathematics, The City College of New York, NAC 8/133, New York, New York 10031
- MR Author ID: 888620
- Email: kbourabee@ccny.cuny.edu
- Martin Kassabov
- Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14850
- Email: kassabov@math.cornell.edu
- Francesco Matucci
- Affiliation: Département de Mathématiques, Faculté des Sciences d’Orsay, Université Paris-Sud 11, Bâtiment 425, Orsay, France
- MR Author ID: 788744
- Email: francesco.matucci@math.u-psud.fr
- Received by editor(s): January 30, 2014
- Received by editor(s) in revised form: October 1, 2014, March 16, 2015, and November 4, 2015
- Published electronically: August 22, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 8343-8367
- MSC (2010): Primary 20F69; Secondary 20E05, 20E07, 20E26, 20E28
- DOI: https://doi.org/10.1090/tran/6865
- MathSciNet review: 3710627