On Sushchansky p-groups - Bondarenko, I.V.; Savchuk, D.M. (Algebra and Discrete Mathematics, 2007)
We study Sushchansky p-groups introduced in
[Sus79]. We recall the original definition and translate it into the
language of automata groups. The original actions of Sushchansky groups on p-ary tree are not level-transitive and we describe
their orbit trees. This allows us to simplify the definition and
prove that these groups admit faithful level-transitive actions on
the same tree. Certain branch structures in their self-similar closures are established. We provide the connection with, so-called,
G groups [BGS03] that shows that all Sushchansky groups have ˇ
intermediate growth and allows to obtain an upper bound on their
period growth functions.