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Groups with infinite FC-center have the Schmidt property

Part of: Ergodic theory Measure-theoretic ergodic theory

Published online by Cambridge University Press:  17 March 2021

YOSHIKATA KIDA Open the ORCID record for YOSHIKATA KIDA [Opens in a new window]  and
ROBIN TUCKER-DROB
YOSHIKATA KIDA*
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Tokyo 153-8914, Japan
ROBIN TUCKER-DROB
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA (e-mail: rtuckerd@math.tamu.edu)
*
e-mail: kida@ms.u-tokyo.ac.jp
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Abstract

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We show that every countable group with infinite finite conjugacy (FC)-center has the Schmidt property, that is, admits a free, ergodic, measure-preserving action on a standard probability space such that the full group of the associated orbit equivalence relation contains a non-trivial central sequence. As a consequence, every countable, inner amenable group with property (T) has the Schmidt property.

Keywords

inner amenable groupsdiscrete p.m.p. equivalence relationscentral sequences

MSC classification

Primary: 37A20: Orbit equivalence, cocycles, ergodic equivalence relations
Secondary: 28D15: General groups of measure-preserving transformations

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 5 , May 2022 , pp. 1662 - 1707
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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