Year: 2025
Type: article
Abstract: Let G be a branch group acting by automorphisms on a rooted tree T. Stabilizers of infinite rays in T are examples of weakly maximal subgroups of G (subgroups that are maximal among subgroups of infinite index), but in general they are not the only examples. In this paper, we describe two families of weakly maximal subgroups of branch groups. We show that, for the first Grigorchuk group as well as for the torsion GGS groups, every weakly maximal subgroup belongs to one of these families. The first family is a generalization of stabilizers of rays, while the second one consists of weakly maximal subgroups with a block structure. We obtain different equivalent characterizations of these families in terms of finite generation, the existence of a trivial rigid stabilizer, the number of orbit-closures for the action on the boundary of the tree or by the means of sections.
Author: Paul-Henry Leemann
Institution: Xi’an Jiaotong-Liverpool University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4409509131