On Sushchansky p-groups

Details On Sushchansky p-groups On Sushchansky p-groups

2006-12-07

arxiv.org/abs/math/0612200v2

Mathematics

Group Theory

14 pages, 3 figures

Scientific paper

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.

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