Stabilizers in Higman-Thompson groups

James Belk, James Hyde, Francesco Matucci

Published 2021-04-12Version 1

We investigate stabilizers of finite sets of rational points in Cantor space for the Higman-Thompson groups $V_{n,r}$. We prove that the pointwise stabilizer is an iterated ascending HNN extension of $V_{n,q}$ for any $q\geq 1$. We also prove that the commutator subgroup of the pointwise stabilizer is simple, and we compute the abelianization. Finally, for each $n$ we classify such pointwise stabilizers up to isomorphism.