作用群为顺从群时无限制圈积的度规逼近
群论
2022-02-17 v4
摘要
我们给出简洁统一的证明，表明弱 sofic 群、sofic 群、线性 sofic 群或超线性群被一个顺从群作无限制圈积后，分别仍为弱 sofic 群、sofic 群、线性 sofic 群或超线性群。借助 Kaloujnine-Krasner 定理，这意味着具有顺从商群的群扩张保持上述四种度规逼近性质。我们还讨论了余顺从群的情形。
引用
@article{arxiv.2004.05735,
title = {Metric approximations of unrestricted wreath products when the acting group is amenable},
author = {Javier Brude and Román Sasyk},
journal= {arXiv preprint arXiv:2004.05735},
year = {2022}
}
备注
v4: Final version. To appear in Communications in Algebra. A new section was added, which deals with the case when a group has a co-amenable subgroup that is weakly sofic, sofic, linear sofic, or hyperlinear, respectively. 13 pages