Groups with infinite FC-center have the Schmidt property
Group Theory
2021-07-01 v3 Dynamical Systems
Operator Algebras
Abstract
We show that every countable group with infinite FC-center has the Schmidt property, i.e., 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 its consequence, every countable, inner amenable group with property (T) has the Schmidt property.
Keywords
Cite
@article{arxiv.1901.08735,
title = {Groups with infinite FC-center have the Schmidt property},
author = {Yoshikata Kida and Robin Tucker-Drob},
journal= {arXiv preprint arXiv:1901.08735},
year = {2021}
}
Comments
47 pages. The referee's comments incorporated (v3). The appendix by the second author was moved to the last section of the text, and the second author joined as a coauthor. The term "FC-radical" was replaced by "FC-center" with the same meaning (v2)