论文标题
汤普森组$ v $的类型系统和最大亚组
Type systems and maximal subgroups of Thompson's group $V$
论文作者
论文摘要
我们介绍了类型系统〜$ \ part $的概念，也就是说，在字母〜$ \ {0,1 \} $上与汤普森（Thompson）的group〜 $ v $的部分操作兼容的有限单词的分区，并将一个子组〜$ \ $ \ ab abt {v} {\ part part} {\ $ v $ V $ companifect我们对有限的简单类型系统进行了分类，并表明各种简单类型系统（包括所有有限简单类型系统）的稳定器是〜$ V $的最大亚组。我们还发现了一个无数的成对非同构最大亚组的家庭。这些最大亚组作为无限简单类型系统的稳定剂出现，并且在先前的文献中尚未描述：具体来说，它们在cantor空间中有限积分的$ v $中并不是稳定器。最后，我们表明，$ v $的子组的两个自然条件（均与原始性相关）仅受$ v $本身的满足，从而提供了新的方法来识别$ v $的子组何时实际上不合适。
We introduce the concept of a type system~$\Part$, that is, a partition on the set of finite words over the alphabet~$\{0,1\}$ compatible with the partial action of Thompson's group~$V$, and associate a subgroup~$\Stab{V}{\Part}$ of~$V$. We classify the finite simple type systems and show that the stabilizers of various simple type systems, including all finite simple type systems, are maximal subgroups of~$V$. We also find an uncountable family of pairwise non-isomorphic maximal subgroups of~$V$. These maximal subgroups occur as stabilizers of infinite simple type systems and have not been described in previous literature: specifically, they do not arise as stabilizers in $V$ of finite sets of points in Cantor space. Finally, we show that two natural conditions on subgroups of $V$ (both related to primitivity) are each satisfied only by $V$ itself, giving new ways to recognise when a subgroup of $V$ is not actually proper.
