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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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.
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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