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...
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| Дата: | 2020 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2020
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/188556 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
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irk-123456789-1885562023-03-07T01:26:54Z On growth of generalized Grigorchuk's overgroups Samarakoon, S.T. 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. 2020 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/188556 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 |
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. |
| format |
Article |
| author |
Samarakoon, S.T. |
| spellingShingle |
Samarakoon, S.T. On growth of generalized Grigorchuk's overgroups Algebra and Discrete Mathematics |
| author_facet |
Samarakoon, S.T. |
| author_sort |
Samarakoon, S.T. |
| title |
On growth of generalized Grigorchuk's overgroups |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2020 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT samarakoonst ongrowthofgeneralizedgrigorchuksovergroups |
| first_indexed |
2023-10-18T23:08:38Z |
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2023-10-18T23:08:38Z |
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1796157360631185408 |