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 de...
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| Datum: | 2018 |
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| Sprache: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/841 |
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admjournalluguniveduua-article-8412018-03-21T11:59:09Z On Sushchansky \(p\)-groups Bondarenko, Ievgen V. Savchuk, Dmytro M. Burnside groups, growth of groups, automata groups, branch groups 20F69, 20F10, 20E08 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 [BGS03] that shows that all Sushchansky groups have intermediate growth and allows to obtain an upper bound on their period growth functions. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/841 Algebra and Discrete Mathematics; Vol 6, No 2 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/841/372 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-03-21T11:59:09Z |
| collection |
OJS |
| language |
English |
| topic |
Burnside groups growth of groups automata groups branch groups 20F69 20F10 20E08 |
| spellingShingle |
Burnside groups growth of groups automata groups branch groups 20F69 20F10 20E08 Bondarenko, Ievgen V. Savchuk, Dmytro M. On Sushchansky \(p\)-groups |
| topic_facet |
Burnside groups growth of groups automata groups branch groups 20F69 20F10 20E08 |
| format |
Article |
| author |
Bondarenko, Ievgen V. Savchuk, Dmytro M. |
| author_facet |
Bondarenko, Ievgen V. Savchuk, Dmytro M. |
| author_sort |
Bondarenko, Ievgen V. |
| title |
On Sushchansky \(p\)-groups |
| title_short |
On Sushchansky \(p\)-groups |
| title_full |
On Sushchansky \(p\)-groups |
| title_fullStr |
On Sushchansky \(p\)-groups |
| title_full_unstemmed |
On Sushchansky \(p\)-groups |
| title_sort |
on sushchansky \(p\)-groups |
| description |
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 [BGS03] that shows that all Sushchansky groups have intermediate growth and allows to obtain an upper bound on their period growth functions. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/841 |
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2025-12-02T15:32:55Z |
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2025-12-02T15:32:55Z |
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1850412237887373312 |