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 has an infinite minimal subflow in its Bernoulli flow . A countably infinite group has an effective minimal subflow in . If is countable and residually finite, then it has such a subflow which is free. We do not know whether there are groups with no free subflows in .

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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:
https://doi.org/10.1090/S0002-9939-09-09905-5

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.