On conjugacy in groups of finite-state automorphisms of rooted trees - Russev, A. V. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
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.