### Relative completions of linear groups over **Z**[t] and **Z**[t,t^{-1}], by Kevin P. Knudson

In this paper we compute the completion of the groups
SL_{n}(**Z**[t]) and SL_{n}(**Z**[t,t^{-1}])
with respect to the obvious homomorphisms to SL_{n}(**Q**); this
is a generalization of the classical Malcev completion (which is trivial
for these groups). It turns out that the obvious guess is the correct one,
namely the proalgebraic group SL_{n}(**Q**[[T]]). We use this
result to study the rational second cohomology of the groups
SL_{n}(R) for R=**Z**[t], **Z**[t,t^{-1}].

Kevin P. Knudson <knudson@math.nwu.edu>