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arXiv · 2112.12428

Two periodicity conditions for spinal groups

Jan Moritz Petschick
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Abstract

A constant spinal group is a subgroup of the automorphism group of a regular rooted tree, generated by a group of rooted automorphisms $A$ and a group of directed automorphisms $B$ whose action on a subtree is equal to the global action. We provide two conditions in terms of certain dynamical systems determined by $A$ and $B$ for constant spinal groups to be periodic, generalising previous results on Grigorchuk--Gupta--Sidki groups and other related constructions. This allows us to provide various new examples of finitely generated infinite periodic groups.

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Jan Moritz Petschick. 2021-12-23. Two periodicity conditions for spinal groups. https://arxiv.org/abs/2112.12428

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