| Abstrakt: |
The groups dVn 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 Vn (D 1Vn) and the Brin-Thompson groups nV (D nV2). A description of the groups Aut.Gn;r / (including the groups Gn;1 D Vn) 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 in 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 Aut.dVn/which extends the description of Aut.1Vn/given in the former paper. We make use of this description to show that Out.dV2/Š Out.V2/o Sd, and more generally give a natural embedding of Out.dVn/into Out.Gn;n1 oSd. [ABSTRACT FROM AUTHOR] |
