On Sushchansky p-groups

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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.
14 pages, 3 figures

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Group Theory, 20F69, 20F10, 20E08

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http://salesiana.dossiersoluciones.com/handle/123456789/128212

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0612200
 http://arxiv.org/abs/math/0612200

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arXiv