G. Elek, THE K-THEORY OF GROMOVS TRANSLATION ALGEBRAS AND THE AMENABILITY OF DISCRETE-GROUPS, Proceedings of the American Mathematical Society, 125(9), 1997, pp. 2551-2553
We prove the following theorem. A finitely generated group Gamma is am
enable if and only if 1 not equal 0 in K-0(T(Gamma)), the algebraic K-
theory group of its translation algebra.