"Groups with infinite FC-center have the Schmidt property."
"Groups with infinite FC-center have the Schmidt property."
复制标题
“具有无限 FC 中心的群具有施密特性质。”
DOI：
10.1017/etds.2020.146
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发表时间：
2022
影响因子：
0.9
通讯作者：
Tucker-Drob, Robin
中科院分区：
文献类型：
--
作者：
Kida, Yoshikata;Tucker-Drob, Robin
我们证明，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，即允许在标准概率空间上进行自由的、遍历的、测度保持的作用，使得相关轨道等价关系的整个群包含一个非平凡的中心序列。因此，每个具有性质 (T) 的可数内部服从群都具有施密特性质。
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.