论文标题
限制亚组和高传递性
Confined subgroups and high transitivity
论文作者
论文摘要
如果$ g $在所有$ k \ geq 1 $的$ k $ tuplass上进行过渡性，则集团$ g $的动作高度传递。许多具有丰富几何或动态作用的群体的例子都接受了高度传递的作用。我们证明，如果一组$ g $承认一项高度传递的操作，以致$ g $不包含限制交替排列的亚组，并且如果$ h $是$ g $的限制亚组，那么$ h $的动作仍然是高度传递性的，可能是在丢弃有限的许多点之后。 该结果提供了一种工具来排除高度传递动作的存在，并分类给定组的高度传递动作。我们在动态起源群体的范围内给出了这些应用的具体插图。特别是，我们获得了有限生成组的高度传递作用的第一个非平凡分类。
An action of a group $G$ is highly transitive if $G$ acts transitively on $k$-tuples of distinct points for all $k \geq 1$. Many examples of groups with a rich geometric or dynamical action admit highly transitive actions. We prove that if a group $G$ admits a highly transitive action such that $G$ does not contain the subgroup of finitary alternating permutations, and if $H$ is a confined subgroup of $G$, then the action of $H$ remains highly transitive, possibly after discarding finitely many points. This result provides a tool to rule out the existence of highly transitive actions, and to classify highly transitive actions of a given group. We give concrete illustrations of these applications in the realm of groups of dynamical origin. In particular we obtain the first non-trivial classification of highly transitive actions of a finitely generated group.
