# Groups with infinite FC-center have the Schmidt property

## TL;DR

This paper proves that countable groups with infinite FC-center possess the Schmidt property, meaning they admit specific measure-preserving actions with non-trivial central sequences, extending to groups with property (T).

## Contribution

It establishes that all countable groups with infinite FC-center have the Schmidt property, including those with property (T), which was previously unknown.

## Key findings

- Countable groups with infinite FC-center have the Schmidt property.
- Inner amenable groups with property (T) also have the Schmidt property.
- The result links group structural properties to dynamical actions with central sequences.

## 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.