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Effective minimal subflows of Bernoulli flows

Author(s): Eli Glasner; Vladimir V. Uspenskij
Journal: Proc. Amer. Math. Soc. 137 (2009), 3147-3154.
MSC (2000): Primary 54H20; Secondary 20E99, 37B10
Posted: April 14, 2009
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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: 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
Posted: April 14, 2009
Additional Notes: The first author is partially supported by BSF grant 2006119
Communicated by: Jane M. Hawkins
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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