In this paper, we introduce the conceptions of multi-transitivity, [Formula: see text]-transitivity and [Formula: see text]-mixing property for free semigroup actions and give some equivalent conditions for a free semigroup action to be multi-transitive, multi-transitive with respect to vectors and strongly multi-transitive, respectively. For instance, we prove that a free semigroup action is multi-transitive or multi-transitive with respect to a vector if and only if its corresponding skew product system is multi-transitive or multi-transitive with respect to the same vector.

中文翻译：

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自由半群动作的多重传递性

在本文中，我们介绍了自由半群作用的多及物性、[公式：见正文]-传递性和[公式：见正文]-混合性质的概念，并给出了自由半群作用具有多传递性的一些等价条件。 ，关于向量的多传递性和强多传递性，分别。例如，我们证明一个自由半群动作对于一个向量是多可传递的或多可传递的当且仅当其对应的斜积系统对于同一向量是多传递的或多传递的。