Conjugacy classes of polyspinal groups
Group Theory
2022-02-04 v2
Abstract
Spinal groups and multi-GGS groups are both generalisations of the well-known Grigorchuk-Gupta-Sidki (GGS-)groups. Here we give a necessary condition for spinal groups to be conjugate, and we establish a necessary and sufficient condition for multi-GGS groups to be conjugate. We also introduce a natural common generalisation of both classes, which we call polyspinal groups. Our results enable us to give a negative answer to a question of Bartholdi, Grigorchuk and Sunik, on whether every finitely generated branch group is isomorphic to a weakly branch spinal group.
Cite
@article{arxiv.2201.03266,
title = {Conjugacy classes of polyspinal groups},
author = {Jan Moritz Petschick and Anitha Thillaisundaram},
journal= {arXiv preprint arXiv:2201.03266},
year = {2022}
}
Comments
12 pages; replaces previous version called "Conjugacy classes of multi-spinal groups"