Let Am be the group of automorphisms of the one-rooted m-ary tree and G be a transitive state-closed subgroup of Am with bounded finite conjugacy classes. We prove that the torsion subgroup Tor(G) has finite exponent and determine an upper bound for the exponent. In case m is a prime number, we prove that G is either a torsion group or a torsion-free abelian group.
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