Further Chameleon Groups of Richard Thompson and Graham Higman: Automorphisms Via Dynamics for the Higman-Thompson Groups $G_{n,r}$

C. Bleak, University of St. Andrews, Scotland, United Kingdom.P. Cameron, University of St. Andrews, Scotland, United Kingdom.Y. Maissel, Ben-Gurion University of the Negev, Beer-Sheva, Israel.A. Navas, University of Santiago de Chile, Chile.F. Olukoya, University of St. Andrews, Scotland, United Kingdom.

• 1. Introduction2. Language, notation, and groups3. More on $G_{n,r,\mathrm {d}}$, $G_{n,r,\mathrm {p}}$, $G_{n,r}$, and $H_{n,r,{\sim }}$4. Local actions5. On the rational group $\mathcal {R}_n$ and the related groups $\mathcal {R}_{n,r}$6. Automorphisms admit few local actions7. Finding our place in the rational group $\mathcal {R}_{n,r}$8. Combinatorial properties of strongly synchronizing transducers9. The natural quotient $\mathcal {B}_{n,r}\twoheadrightarrow \mathcal {O}_{n,r}$10. Root functions and detecting flavours of synchronicity11. Open problemsA. The inversion construction