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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Effective minimal subflows of Bernoulli flows


Authors: Eli Glasner and Vladimir V. Uspenskij
Journal: Proc. Amer. Math. Soc. 137 (2009), 3147-3154
MSC (2000): Primary 54H20; Secondary 20E99, 37B10
Published electronically: April 14, 2009
MathSciNet review: 2506474
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Abstract: We show that every infinite discrete group $ G$ has an infinite minimal subflow in its Bernoulli flow $ \{0,1\}^G$. A countably infinite group $ G$ has an effective minimal subflow in $ \{0,1\}^G$. If $ G$ is countable and residually finite, then it has such a subflow which is free. We do not know whether there are groups $ G$ with no free subflows in $ \{0,1\}^G$.


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Additional Information

Eli Glasner
Affiliation: Department of Mathematics, Tel-Aviv University, Tel Aviv, Israel
Email: glasner@math.tau.ac.il

Vladimir V. Uspenskij
Affiliation: Department of Mathematics, 321 Morton Hall, Ohio University, Athens, Ohio 45701
Email: uspensk@math.ohiou.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09905-5
PII: S 0002-9939(09)09905-5
Keywords: Bernoulli flow, free actions, symbolically-free groups
Received by editor(s): June 19, 2007
Received by editor(s) in revised form: December 14, 2007
Published electronically: April 14, 2009
Additional Notes: The first author is partially supported by BSF grant 2006119
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.