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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Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2007
Hauptverfasser: Bondarenko, I.V., Savchuk, D.M.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2007
Online Zugang: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
Zitieren: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
id nasplib_isofts_kiev_ua-123456789-157340
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title On Sushchansky p-groups
spellingShingle On Sushchansky p-groups
Bondarenko, I.V.
Savchuk, D.M.
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
author Bondarenko, I.V.
Savchuk, D.M.
author_facet Bondarenko, I.V.
Savchuk, D.M.
publishDate 2007
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
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.
issn 1726-3255
url https://nasplib.isofts.kiev.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.
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