On growth of generalized Grigorchuk's overgroups
Grigorchuk’s Overgroup Ĝ, is a branch group of intermediate growth. It contains the first Grigorchuk’s torsion group G of intermediate growth constructed in 1980, but also has elements of infinite order. Its growth is substantially greater than the growth of G. The group G, corresponding to the sequ...
Gespeichert in:
| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2020 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2020
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/188556 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On growth of generalized Grigorchuk's overgroups / S.T. Samarakoon // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 97–117. — Бібліогр.: 20 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-188556 |
|---|---|
| record_format |
dspace |
| spelling |
Samarakoon, S.T. 2023-03-05T17:34:30Z 2023-03-05T17:34:30Z 2020 On growth of generalized Grigorchuk's overgroups / S.T. Samarakoon // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 97–117. — Бібліогр.: 20 назв. — англ. 1726-3255 DOI:10.12958/adm1451 2010 MSC: 20E08 https://nasplib.isofts.kiev.ua/handle/123456789/188556 Grigorchuk’s Overgroup Ĝ, is a branch group of intermediate growth. It contains the first Grigorchuk’s torsion group G of intermediate growth constructed in 1980, but also has elements of infinite order. Its growth is substantially greater than the growth of G. The group G, corresponding to the sequence (012)∞ = 012012 . . ., is a member of the family {Gω|ω ∈ Ω = {0, 1, 2}ᴺ} consisting of groups of intermediate growth when sequence ω is not eventually constant. Following this construction, we define the family { Ĝω, ω ∈ Ω} of generalized overgroups. Then Ĝ = Ĝ (012)∞ and Gω is a subgroup of Ĝω for each ω ∈ Ω. We prove, if ω is eventually constant, then Ĝω is of polynomial growth and if ω is not eventually constant, then Ĝω is of intermediate growth. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On growth of generalized Grigorchuk's overgroups Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On growth of generalized Grigorchuk's overgroups |
| spellingShingle |
On growth of generalized Grigorchuk's overgroups Samarakoon, S.T. |
| title_short |
On growth of generalized Grigorchuk's overgroups |
| title_full |
On growth of generalized Grigorchuk's overgroups |
| title_fullStr |
On growth of generalized Grigorchuk's overgroups |
| title_full_unstemmed |
On growth of generalized Grigorchuk's overgroups |
| title_sort |
on growth of generalized grigorchuk's overgroups |
| author |
Samarakoon, S.T. |
| author_facet |
Samarakoon, S.T. |
| publishDate |
2020 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
Grigorchuk’s Overgroup Ĝ, is a branch group of intermediate growth. It contains the first Grigorchuk’s torsion group G of intermediate growth constructed in 1980, but also has elements of infinite order. Its growth is substantially greater than the growth of G. The group G, corresponding to the sequence (012)∞ = 012012 . . ., is a member of the family {Gω|ω ∈ Ω = {0, 1, 2}ᴺ} consisting of groups of intermediate growth when sequence ω is not eventually constant. Following this construction, we define the family { Ĝω, ω ∈ Ω} of generalized overgroups. Then Ĝ = Ĝ (012)∞ and Gω is a subgroup of Ĝω for each ω ∈ Ω. We prove, if ω is eventually constant, then Ĝω is of polynomial growth and if ω is not eventually constant, then Ĝω is of intermediate growth.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/188556 |
| citation_txt |
On growth of generalized Grigorchuk's overgroups / S.T. Samarakoon // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 97–117. — Бібліогр.: 20 назв. — англ. |
| work_keys_str_mv |
AT samarakoonst ongrowthofgeneralizedgrigorchuksovergroups |
| first_indexed |
2025-12-01T02:43:23Z |
| last_indexed |
2025-12-01T02:43:23Z |
| _version_ |
1850859109260197888 |