Two periodicity conditions for spinal groups

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.