Compositio Mathematica

Table of Contents - May 2012 - Volume 148, Issue 03  

Research Article

Quantifying residual finiteness of arithmetic groups

Khalid Bou-Rabeea1 and Tasho Kalethaa2

a1 Department of Mathematics, University of Chicago, 5734 University Ave., Chicago, IL 60637, USA (email: khalid@math.uchicago.edu)

a2 Department of Mathematics, University of Chicago, 5734 University Ave., Chicago, IL 60637, USA (email: tkaletha@math.uchicago.edu)

Abstract

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).

(Received September 16 2010)

(Accepted May 12 2011)

(Online publication March 19 2012)

2010 Mathematics Subject Classification

  • 20E26 (primary);
  • 11F06;
  • 22E40;
  • 20H05 (secondary)

Keywords

  • arithmetic groups;
  • normal residual finiteness growth;
  • residual finiteness