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- W4287668835 abstract "The groups $dV_n$ are an infinite family of groups, first introduced by C. Mart'inez-P'erez, 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 $operatorname{Out}(G_{n, n-1})wr S_d$." @default.
- W4287668835 created "2022-07-25" @default.
- W4287668835 creator A5055221465 @default.
- W4287668835 date "2020-09-11" @default.
- W4287668835 modified "2023-09-28" @default.
- W4287668835 title "A Description of Aut(dVn) and Out(dVn) Using Transducers" @default.
- W4287668835 doi "https://doi.org/10.48550/arxiv.2009.05450" @default.
- W4287668835 hasPublicationYear "2020" @default.
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