The further chameleon groups of Richard Thompson and Graham Higman : automorphisms via dynamics for the Higman-Thompson groups Gn,r / C. Bleak, P. Cameron, Y. Maissel, A. Navas, F. Olukoya.

Format:

Book

Author/Creator:

Bleak, Collin, author.

Cameron, Peter J. (Peter Jephson), 1947- author.

Maissel, Yonah, author.

Navas, Andrés, author.

Olukoya, Feyishayo, author.

Series:

Memoirs of the American Mathematical Society ; v. 1510.

Memoirs of the American Mathematical Society ; v. 1510

Language:

English

Subjects (All):

Group theory.

Physical Description:

vii, 94 pages : illustrations ; 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2024.

Summary:

We describe, through the use of Rubin's theorem, the automorphism groups of the Higman-Thompson groups Gn,r as groups of specific homeomorphisms of Cantor spaces Cn,r. This continues a thread of research begun by Brin, and extended later by Brin and Guzmán: to characterise the automorphism groups of the 'Chameleon groups of Richard Thompson,' as Brin referred to them in 1996. The work here completes the first stage of that twenty-year-old program, containing (amongst other things) a characterisation of the automorphism group of V, which was the "last chameleon." The homeomorphisms which arise fit naturally into the framework of Grigorchuk, Nekrashevich, and Suschanskiĭ's rational group of transducers: they are exactly those homeomorphisms which are induced by bi-synchronizing transducers, which we define in the paper. This result appears to offer insight into the nature of Brin and Guzmán's exotic automorphisms, while also uncovering connections with the theory of reset words for automata (arising in the Road Colouring Problem) and with the theory of automorphism groups of the full shift.

Notes:

"September 2024 ; vol. 301 number 1510 (fourth of 7 numbers)".

Includes bibliographical references (pages 91-92) and index.

ISBN:

1470471450

9781470471453

OCLC:

1467832307