We describe subgroups and overgroups of the generalized Thompson groups [Formula: see text] which arise via conjugation by rational homeomorphisms of Cantor space. We specifically consider conjugating [Formula: see text] by homeomorphisms induced by synchronizing transducers and their inverses. Our descriptions of the subgroups and overgroups use properties of the conjugating transducer to either restrict or augment the action of [Formula: see text] on Cantor space. We also consider a class [Formula: see text] of transducers containing all invertible, initial transducers. We associate to every transducer [Formula: see text] in this class, a group [Formula: see text]. We show that for a certain subclass of [Formula: see text], the groups [Formula: see text] are simple.

中文翻译：

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Vn 的共轭子群和超群

我们描述了广义 Thompson 群的子群和超群 [公式：见正文]，它们通过康托空间的理性同胚共轭而产生。我们特别考虑通过同步换能器及其逆引起的同胚共轭[公式：见文本]。我们对子群和超群的描述使用共轭转换器的属性来限制或增强 [公式：见文本] 在康托空间上的作用。我们还考虑包含所有可逆的初始传感器的传感器类[公式：参见文本]。我们将这个类中的每个换能器 [公式：参见文本] 关联到一个组 [公式：参见文本]。我们证明对于 [Formula: see text] 的某个子类，组 [Formula: see text] 是简单的。