Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank over noetherian rings

Authors:
Andrei S. Rapinchuk and Igor A. Rapinchuk

Journal:
Proc. Amer. Math. Soc. **139** (2011), 3099-3113

MSC (2010):
Primary 19B37; Secondary 20G35

DOI:
https://doi.org/10.1090/S0002-9939-2011-10736-6

Published electronically:
January 20, 2011

MathSciNet review:
2811265

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Abstract: Let be a universal Chevalley-Demazure group scheme associated to a reduced irreducible root system of rank For a commutative ring , we let denote the elementary subgroup of the group of -points The congruence kernel is then defined to be the kernel of the natural homomorphism where is the profinite completion of and is the congruence completion defined by ideals of finite index. The purpose of this paper is to show that for an arbitrary noetherian ring (with some minor restrictions if is of type or ), the congruence kernel is central in

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Additional Information

**Andrei S. Rapinchuk**

Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904

Email:
asr3x@virginia.edu

**Igor A. Rapinchuk**

Affiliation:
Department of Mathematics, Yale University, New Haven, Connecticut 06502

Email:
igor.rapinchuk@yale.edu

DOI:
https://doi.org/10.1090/S0002-9939-2011-10736-6

Received by editor(s):
July 22, 2010

Received by editor(s) in revised form:
August 12, 2010

Published electronically:
January 20, 2011

Communicated by:
Jonathan I. Hall

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.