论文标题
使用传感器的AUT（DVN）和OUT（DVN）的描述
A Description of Aut(dVn) and Out(dVn) Using Transducers
论文作者
论文摘要
$ dv_n $的组是一个无限的团体家族，首先由C.Martínez-Pérez，F。Matucci和B. E. A. Nucinkis介绍，其中包括Higman-Thompson组$ v_n（= 1V_N）$和Brin-Thompson $ nv（= NV_2）$。 $ \ operatorname {aut}（g_ {n，r}）$的组描述（包括$ g_ {n，1} = v_n $）。他们的描述使用Cantor Space同态的传感器表示，引入了R. I. Grigorchuk，V。V。Nekrashevich和V. I. Sushchanskii的论文，以及M. Rubin的定理。我们概括了后一篇论文的换能器，并利用这些传感器来提供$ \ operatatorName {aut}（dv_n）$的描述，该$扩展了$ \ operatatorName {aut}（aut}（1V_N）$的描述。我们利用此描述表明$ \ permatorName {out}（dv_2）\ cong \ permatorAtorname {out}（out}（v_2）\ wr s_d $，并且更通常将$ \ operatatorNamame {out}（out out}（out}（dv_n）$的自然嵌入到$ \ operaTornArmame {dv_n）中$ \ operaTornAmeAmeAmeAmeAme {ext} n-1
The groups $dV_n$ are an infinite family of groups, first introduced by C. Martínez-Pérez, F. Matucci and B. E. A. Nucinkis, which includes both the Higman-Thompson groups $V_n(=1V_n)$ and the Brin-Thompson groups $nV(=nV_2)$. A description of the groups $\operatorname{Aut}(G_{n, r})$ (including the groups $G_{n,1}=V_n$) has previously been given by C. Bleak, P. Cameron, Y. Maissel, A. Navas, and F. Olukoya. Their description uses the transducer representations of homeomorphisms of Cantor space introduced a paper of R. I. Grigorchuk, V. V. Nekrashevich, and V. I. Sushchanskii, together with a theorem of M. Rubin. We generalise the transducers of the latter paper and make use of these transducers to give a description of $\operatorname{Aut}(dV_n)$ which extends the description of $\operatorname{Aut}(1V_n)$ given in the former paper. We make use of this description to show that $\operatorname{Out}(dV_2) \cong \operatorname{Out}(V_2)\wr S_d$, and more generally give a natural embedding of $\operatorname{Out}(dV_n)$ into $\operatorname{Out}(G_{n, n-1})\wr S_d$.
