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...
Збережено в:
| Дата: | 2007 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2007
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
irk-123456789-157340 |
|---|---|
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dspace |
| spelling |
irk-123456789-1573402019-06-21T01:30:23Z On Sushchansky p-groups Bondarenko, I.V. Savchuk, D.M. 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. 2007 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/157340 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Bondarenko, I.V. Savchuk, D.M. |
| spellingShingle |
Bondarenko, I.V. Savchuk, D.M. On Sushchansky p-groups Algebra and Discrete Mathematics |
| author_facet |
Bondarenko, I.V. Savchuk, D.M. |
| author_sort |
Bondarenko, I.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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/157340 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT bondarenkoiv onsushchanskypgroups AT savchukdm onsushchanskypgroups |
| first_indexed |
2023-05-20T17:52:30Z |
| last_indexed |
2023-05-20T17:52:30Z |
| _version_ |
1796154293285289984 |