This article is cited in 2 papers

RESEARCH ARTICLE

On Sushchansky $p$-groups

Ievgen V. Bondarenko^ab, Dmytro M. Savchuk<sup>a

a</sup> Kyiv Taras Shevchenko University, Ukraine and Texas A&M University, USA
^b Kyiv Taras Shevchenko University, Ukraine

Abstract: 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.

MSC: 20F69, 20F10, 20E08

Language: English

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