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Quantifying residual finiteness of arithmetic groups

Part of: Other groups of matrices Discontinuous groups and automorphic forms Structure and classification of infinite or finite groups Lie groups

Published online by Cambridge University Press:  19 March 2012

Khalid Bou-Rabee  and
Tasho Kaletha
Khalid Bou-Rabee
Affiliation:
Department of Mathematics, University of Chicago, 5734 University Ave., Chicago, IL 60637, USA (email: khalid@math.uchicago.edu)
Tasho Kaletha
Affiliation:
Department of Mathematics, University of Chicago, 5734 University Ave., Chicago, IL 60637, USA (email: tkaletha@math.uchicago.edu)
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Abstract

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The normal residual finiteness growth of a group quantifies how well approximated the group is by its finite quotients. We show that any S-arithmetic subgroup of a higher rank Chevalley group G has normal residual finiteness growth ndim (G).

Keywords

arithmetic groupsnormal residual finiteness growthresidual finiteness

MSC classification

Secondary: 20E26: Residual properties and generalizations; residually finite groups 11F06: Structure of modular groups and generalizations; arithmetic groups 22E40: Discrete subgroups of Lie groups 20H05: Unimodular groups, congruence subgroups
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 3 , May 2012 , pp. 907 - 920
Copyright
Copyright © Foundation Compositio Mathematica 2012

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