Geodesic
On Sushchansky $p$-groups
Algebra and discrete mathematics, no. 2 (2007), pp. 22-42 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, $\mathsf G$ groups [BGŠ03] that shows that all Sushchansky groups have intermediate growth and allows to obtain an upper bound on their period growth functions.
Keywords: Burnside groups, growth of groups, automata groups, branch groups. 
@article{ADM_2007_2_a3,
     author = {Ievgen V. Bondarenko and Dmytro M. Savchuk},
     title = {On {Sushchansky} $p$-groups},
     journal = {Algebra and discrete mathematics},
     pages = {22--42},
     year = {2007},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2007_2_a3/}
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Ievgen V. Bondarenko; Dmytro M. Savchuk. On Sushchansky $p$-groups. Algebra and discrete mathematics, no. 2 (2007), pp. 22-42. http://geodesic.mathdoc.fr/item/ADM_2007_2_a3/