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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188556 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862640327491321856 |
|---|---|
| author | Samarakoon, S.T. |
| author_facet | Samarakoon, S.T. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-01T02:43:23Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188556 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-01T02:43:23Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| 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 |
| spellingShingle | On growth of generalized Grigorchuk's overgroups Samarakoon, S.T. |
| title | 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_short | On growth of generalized Grigorchuk's overgroups |
| title_sort | on growth of generalized grigorchuk's overgroups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188556 |
| work_keys_str_mv | AT samarakoonst ongrowthofgeneralizedgrigorchuksovergroups |