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Intersection growth in groups


Authors: Ian Biringer, Khalid Bou-Rabee, Martin Kassabov and Francesco Matucci
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
Published electronically: August 22, 2017
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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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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
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
Email: francesco.matucci@math.u-psud.fr

DOI: https://doi.org/10.1090/tran/6865
Keywords: Residually finite groups, growth in groups, intersection growth, residual finiteness growth
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
Article copyright: © Copyright 2017 American Mathematical Society

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