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CHARACTERIZATIONS OF LOCALLY FINITE ACTIONS OF GROUPS ON SETS

Published online by Cambridge University Press:  04 September 2017

EDUARDO SCARPARO
EDUARDO SCARPARO*
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen, Denmark e-mail: duduscarparo@gmail.com
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Abstract

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We show that an action of a group on a set X is locally finite if and only if X is not equidecomposable with a proper subset of itself. As a consequence, a group is locally finite if and only if its uniform Roe algebra is finite.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 2 , May 2018 , pp. 285 - 288
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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