A new characterization of amenable groups
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- by Jon Sherman PDF
- Trans. Amer. Math. Soc. 254 (1979), 365-389 Request permission
Abstract:
Paradoxical sets, which are a natural generalization of the type of sets made famous as Hausdorff-Banach-Tarski paradoxes, are defined in terms of piecewise translations. Piecewise translations are the generalization to arbitrary discrete groups of the maps used in the Banach-Tarski paradoxes as congruences by finite decomposition. A subset of a group is defined to be large if finitely many translates of it can cover the group. The main result of this paper is that a group is amenable if and only if it does not contain a large paradoxical set.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 254 (1979), 365-389
- MSC: Primary 43A07; Secondary 28A12, 47D05
- DOI: https://doi.org/10.1090/S0002-9947-1979-0539924-7
- MathSciNet review: 539924