Groups with infinite FC-center have the Schmidt property

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.

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)