The -theory of Gromov's translation algebras and the amenability of discrete groups

Author:
Gábor Elek

Journal:
Proc. Amer. Math. Soc. **125** (1997), 2551-2553

MSC (1991):
Primary 20F38

DOI:
https://doi.org/10.1090/S0002-9939-97-04056-2

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Abstract: We prove the following theorem. A finitely generated group is amenable if and only if in , the algebraic -theory group of its translation algebra.

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Additional Information

**Gábor Elek**

Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47906

Address at time of publication:
Mathematical Institute, Hungarian Academy of Science, P. O. Box 127, H-1364 Budapest, Hungary

Email:
elekgab@math.purdue.edu, elek@math-inst.hu

DOI:
https://doi.org/10.1090/S0002-9939-97-04056-2

Received by editor(s):
April 9, 1996

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1997
American Mathematical Society