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ISSN 1088-6850(e) ISSN 0002-9947(p)

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

Author(s): Kevin P. Knudson
Journal: Trans. Amer. Math. Soc. 352 (2000), 2205-2216.
MSC (1991): Primary 55P60, 20G35, 20H05; Secondary 20G10, 20F14
Posted: July 26, 1999
Correction(s): Tran. Amer. Math. Soc. 353 (2001), 3833-3834.
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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