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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Relative completions of linear groups
over ${\mathbb Z}[t]$ and ${\mathbb Z}[t,t^{-1}]$


Author: Kevin P. Knudson
Journal: Trans. Amer. Math. Soc. 352 (2000), 2205-2216
MSC (1991): Primary 55P60, 20G35, 20H05; Secondary 20G10, 20F14
Published electronically: July 26, 1999
MathSciNet review: 1641103
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Abstract | References | Similar Articles | Additional Information

Abstract: We compute the completion of the groups $SL_n({\mathbb Z}[t])$ and
$SL_n({\mathbb Z}[t,t^{-1}])$ relative to the obvious homomorphisms to $SL_n({\mathbb Q})$; this is a generalization of the classical Malcev completion. We also make partial computations of the rational second cohomology of these groups.


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Additional Information

Kevin P. Knudson
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Address at time of publication: Department of Mathematics, Wayne State University, Detroit, Michigan 48202

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02433-2
PII: S 0002-9947(99)02433-2
Received by editor(s): January 20, 1998
Published electronically: July 26, 1999
Additional Notes: Supported by an NSF Postdoctoral Fellowship, grant no. DMS-9627503
Article copyright: © Copyright 2000 American Mathematical Society