Conjugacy classes of polyspinal groups

2022/01/10 by Petschick, Jan Moritz, Thillaisundaram, Anitha · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2201.03266

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.

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• Normal subgroups of non-torsion multi-EGS groups

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