We show that the conjugacy of elements of finite order in the group of finite-state automorphisms of a rooted tree is equivalent to their conjugacy in the group of all automorphisms of the rooted tree. We establish a criterion for conjugacy between a finite-state automorphism and the adding machine in the group of finite-state automorphisms of a rooted tree of valency 2.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1357–1366, October, 2008.
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Russev, A.V. On conjugacy in groups of finite-state automorphisms of rooted trees. Ukr Math J 60, 1581–1591 (2008). https://doi.org/10.1007/s11253-009-0156-6
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DOI: https://doi.org/10.1007/s11253-009-0156-6