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A note on the Følner condition for amenability

Published online by Cambridge University Press:  22 January 2016

Toshiaki Adachi
Toshiaki Adachi*
Affiliation:
Department of Mathematics Nagoya Institute of Technology, Showa-ku, Nagoya 466, Japan e-mail address: [email protected]
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Let G be a countably generated discrete group. A right-invariant mean μ on G is a bounded linear functional of the space L∞(G) of bounded functions on G having the property:

We say that G is amenable if it is equipped with a right-invariant mean. Finite groups, abelian groups, in fact, groups of subexponential growth are amenable. Solvable group are also amenable. Subgroups and quotients of amenable groups are amenable. On the other hand, free groups having two generators and over are non-amenable.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 131 , September 1993 , pp. 67 - 74
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

References

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[6] Paterson, A. L., Amenability, Methematical Surveys and Monographs 29, A.M.S 1988.Google Scholar