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...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2007 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2007
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/157340 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862744450344681472 |
|---|---|
| author | Bondarenko, I.V. Savchuk, D.M. |
| author_facet | Bondarenko, I.V. Savchuk, D.M. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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,
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.
|
| first_indexed | 2025-12-07T20:35:24Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-157340 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T20:35:24Z |
| publishDate | 2007 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Bondarenko, I.V. Savchuk, D.M. 2019-06-20T02:39:29Z 2019-06-20T02:39:29Z 2007 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. 1726-3255 2000 Mathematics Subject Classification: 20F69, 20F10, 20E08. https://nasplib.isofts.kiev.ua/handle/123456789/157340 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. Both authors were partially supported by NSF grants DMS-0308985 and DMS0456185 en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On Sushchansky p-groups Article published earlier |
| spellingShingle | On Sushchansky p-groups Bondarenko, I.V. Savchuk, D.M. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/157340 |
| work_keys_str_mv | AT bondarenkoiv onsushchanskypgroups AT savchukdm onsushchanskypgroups |