Relative completions of linear groups over ℤ[𝕥] and ℤ[𝕥,𝕥⁻¹]

Knudson, Kevin

doi:10.1090/S0002-9947-99-02433-2

Relative completions of linear groups over $\mathbb {Z}[t]$ and $\mathbb {Z}[t,t^{-1}]$
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by Kevin P. Knudson PDF

Trans. Amer. Math. Soc. 352 (2000), 2205-2216 Request permission

Correction: Trans. Amer. Math. Soc. 353 (2001), 3833-3834.

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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