论文标题
关于汤普森组的最大亚组
On Maximal Subgroups of Thompson's Group $F$
论文作者
论文摘要
我们通过与它们相关的自动机研究汤普森组$ f $的子组。我们证明，无限索引的$ f $ $ f $的每个最大子组已关闭，也就是说，它与与之相关的自动机接受的$ f $的子组一致。因此，每个有限生成的$ f $的最大亚组都没有以$ f $为单位。我们还证明，每一个有限生成的$ f $的亚组都包含在有限生成的$ f $的最大亚组中，并构建了一个无i晶状体最大亚组的无限型无限亚组的无限亚组。
We study subgroups of Thompson's group $F$ by means of an automaton associated with them. We prove that every maximal subgroup of $F$ of infinite index is closed, that is, it coincides with the subgroup of $F$ accepted by the automaton associated with it. It follows that every finitely generated maximal subgroup of $F$ is undistorted in $F$. We also prove that every finitely generated subgroup of $F$ is contained in a finitely generated maximal subgroup of $F$ and construct an infinite family of non-isomorphic maximal subgroups of infinite index in $F$.
