Abstract
G(Fq((x))((t))) = G(Fq((x))[[t]])G(Fq [[x]]((t))). Here G is an arbitrary connected linear reductive group, Fq is a finite field, and for an arbitrary field k by k((x)) and k[[x]] we denote the fields of Laurent and Taylor power series, respectively, with coefficients in k. In the present paper, we prove this lemma for G = GL(n) by elementary methods. Note that the assertion is not always true for nonreductive groups G. For example, if G is a onedimensional additive group, then it is not true that
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