%0 Journal Article
%T On Sushchansky p-groups
%A Ievgen Bondarenko
%A Dmytro Savchuk
%J Mathematics
%D 2006
%I arXiv
%X We study Sushchansky p-groups. 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 that shows that all Sushchansky groups have intermediate growth and allows to obtain an upper bound on their period growth functions.
%U http://arxiv.org/abs/math/0612200v2