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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| Format: | Artikel |
| Sprache: | Englisch |
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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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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543072103432192 |
|---|---|
| author | Bondarenko, Ievgen V. Savchuk, Dmytro M. |
| author_facet | Bondarenko, Ievgen V. Savchuk, Dmytro M. |
| author_sort | Bondarenko, Ievgen V. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T11:59:09Z |
| 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. |
| first_indexed | 2025-12-02T15:32:55Z |
| format | Article |
| id | admjournalluguniveduua-article-841 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:32:55Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | 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 |
| spellingShingle | Burnside groups growth of groups automata groups branch groups 20F69 20F10 20E08 Bondarenko, Ievgen V. Savchuk, Dmytro M. On Sushchansky \(p\)-groups |
| title | On Sushchansky \(p\)-groups |
| title_full | On Sushchansky \(p\)-groups |
| title_fullStr | On Sushchansky \(p\)-groups |
| title_full_unstemmed | On Sushchansky \(p\)-groups |
| title_short | On Sushchansky \(p\)-groups |
| title_sort | on sushchansky \(p\)-groups |
| topic | Burnside groups growth of groups automata groups branch groups 20F69 20F10 20E08 |
| topic_facet | Burnside groups growth of groups automata groups branch groups 20F69 20F10 20E08 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/841 |
| work_keys_str_mv | AT bondarenkoievgenv onsushchanskypgroups AT savchukdmytrom onsushchanskypgroups |