An automata theoretic proof that \mathopOut(T) ≅ ℤ/2ℤ and some embedding results for \mathopOut(V)

2020/03/31 by Feyishayo Olukoya, Olukoya, Feyishayo
Biochemistry, Genetics and Molecular Biology · Computer Science · #20E07 #20E32 #20E36 #20F10 #Cellular Automata and Applications #DNA and Biological Computing #FOS: Mathematics #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2003.14372

openalex publication_date 2020/03/31 · openalex created_date 2020/04/10 · openalex updated_date 2026/07/28

Abstract

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 ≥ 3 and 1 ≤ r < n the outerautomorphism groups of G_n,r and T_n,r contain an isomorphic copy of F.

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• A Description of Aut(dVn) and Out(dVn) Using Transducers
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• The further chameleon groups of Richard Thompson and Graham Higman: Automorphisms via dynamics for the Higman groups G_n,r
• Automorphisms of the two-sided shift and the Higman--Thompson groups III: extensions