论文标题
自动机理论证明$ \ mathop {\ mathrm {out}}（t）\ cong \ mathbb {z}/2 \ mathbb {z} $以及$ \ mathop {\ mathop {\ mathrm {out}}}（v）$的一些嵌入结果
An automata theoretic proof that $\mathop{\mathrm{Out}}(T) \cong \mathbb{Z}/2\mathbb{Z}$ and some embedding results for $\mathop{\mathrm{Out}}(V)$
论文作者
论文摘要
在一份开创性的论文中，布林证明了汤普森集团$ t $的外肌形态群对第二阶循环群是同构。在本文中，基于将希格曼 - 汤普森（Higman-Thompson）组的自动形态表征为$ g_ {n，r} $和$ t_ {n，r} $作为传感器组，我们给出了一个新的证明，本质上，自动机理论，是布林的结果。 我们还证明，汤普森组的$ v = g_ {2,1} $的外肌形畸形组包含汤普森组$ f $的同构副本。这扩展了作者的结果，表明每当$ n \ ge 3 $和$ 1 \ le r <n $时，$ g_ {n，r} $和$ t_ {n，r} $的ofterautomormorphism ofter组包含$ f $的同构副本。
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 $F$.
