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.

中文翻译：

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具有无限 FC 中心的群具有施密特性质

我们证明了每个具有无限有限共轭（FC）中心的可数群都具有施密特性质，即在标准概率空间上允许自由的、遍历的、保测的作用，使得相关轨道等价关系的完整群包含一个非平凡的中心序列。因此，每个具有属性 (T) 的可数、内部顺从群都具有施密特属性。