The Strong Approximation Conjecture holds for amenable groups
نویسنده
چکیده
Let G be a finitely generated group and G⊲G1⊲G2⊲. . . be normal subgroups such that ∩k=1Gk = {1}. Let A ∈ Mat d×d(CG) and Ak ∈ Mat d×d(C(G/Gk)) be the images of A under the maps induced by the epimorphisms G → G/Gk. According to the strong form of the Approximation Conjecture of Lück [4] dimG(ker A) = lim k→∞ dimG/Gk(ker Ak) , where dimG denotes the von Neumann dimension. In [2] Dodziuk, Linnell, Mathai, Schick and Yates proved the conjecture for torsion free elementary amenable groups. In this paper we extend their result for all amenable groups, using the quasi-tilings of Ornstein and Weiss [6]. AMS Subject Classifications: 46L10, 43A07
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