$\mathop{\mathrm{Out}}(T) \cong \mathbb{Z}/2\mathbb{Z}$的自动机理论证明和$\mathop{\mathrm{Out}}(V)$的嵌入结果
An automata theoretic proof that $\mathop{\mathrm{Out}}(T) \cong \mathbb{Z}/2\mathbb{Z}$ and some embedding results for $\mathop{\mathrm{Out}}(V)$
摘要：
在一篇开创性的论文中，布林证明了汤普森群$T$的外自同构群同构于二阶的循环群。在本文中，在Higman-Thompson群$G_{n,r}$和$T_{n,r}$的自同构作为变换器群的特征的基础上，我们对布林的结果给出了一个本质上是自动机理论的新证明。我们还证明了Thompson群$V = G_{2,1}$的外自同构群包含Thompson群$F$的同构副本。这推广了作者的一个结果，即只要$n \ge 3$和$1 \le r < n$，$G_{n,r}$和$T_{n,r}$的外自同构群就包含$F$的同构拷贝.
英文摘要：
In a seminal paper, Brin demonstrates that the outerautomorphism group of Thompson group $T$ is isomorphic to the cyclic group of order two. In this article, building on characterisation of automorphisms of the Higman-Thompson groups $G_{n,r}$ and $T_{n,r}$ as groups of transducers, we give a new proof, automata theoretic in nature, of Brin's result. We also demonstrate that the group of outerautomorphisms of Thompson's group $V = G_{2,1}$ contains an isomorphic copy of Thompson's group $F$. This extends a result of the author demonstrating that whenever $n \ge 3$ and $1 \le r < n$ the outerautomorphism groups of $G_{n,r}$ and $T_{n,r}$ contain an isomorphic copy of $F$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
