具有无限 FC-中心的群满足 Schmidt 性质
群论
2021-07-01 v3 动力系统
算子代数
摘要
我们证明每个具有无限 FC-中心的可数群都满足 Schmidt 性质，即允许在标准概率空间上执行一个自由、遍历且保测的作用，使得相关轨道等价关系的全群包含一个非平凡的中心序列。作为其推论，每个具有性质 (T) 的可数内顺从群都满足 Schmidt 性质。
引用
@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}
}
备注
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)