On Sushchansky p-groups
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 definit...
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| Date: | 2007 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2007
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/157340 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Sushchansky p-groups / I.V. Bondarenko, D.M. Savchuk // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 2. — С. 22–42. — Бібліогр.: 28 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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,
G groups [BGS03] that shows that all Sushchansky groups have ˇ
intermediate growth and allows to obtain an upper bound on their
period growth functions. |
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