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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Effective minimal subflows of Bernoulli flows
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by Eli Glasner and Vladimir V. Uspenskij PDF
Proc. Amer. Math. Soc. 137 (2009), 3147-3154 Request permission

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
  • MR Author ID: 271825
  • Email: glasner@math.tau.ac.il
  • Vladimir V. Uspenskij
  • Affiliation: Department of Mathematics, 321 Morton Hall, Ohio University, Athens, Ohio 45701
  • MR Author ID: 191555
  • Email: uspensk@math.ohiou.edu
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 3147-3154
  • MSC (2000): Primary 54H20; Secondary 20E99, 37B10
  • DOI: https://doi.org/10.1090/S0002-9939-09-09905-5
  • MathSciNet review: 2506474