Prethick subsets in partitions of groups
A subset S of a group G is called thick if, for any finite subset F of G, there exists g ∈ G such that Fg ⊆ S, and k-prethick, k ∈ N if there exists a subset K of G such that |K| = k and KS is thick. For every finite partition P of G, at least one cell of P is k-prethick for some k ∈ N. We show that...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2012 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/152243 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Prethick subsets in partitions of groups / I.V. Protasov, S. Slobodianiuk // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 267–275. — Бібліогр.: 18 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862740103836729344 |
|---|---|
| author | Protasov, I.V. Slobodianiuk, S. |
| author_facet | Protasov, I.V. Slobodianiuk, S. |
| citation_txt | Prethick subsets in partitions of groups / I.V. Protasov, S. Slobodianiuk // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 267–275. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | A subset S of a group G is called thick if, for any finite subset F of G, there exists g ∈ G such that Fg ⊆ S, and k-prethick, k ∈ N if there exists a subset K of G such that |K| = k and KS is thick. For every finite partition P of G, at least one cell of P is k-prethick for some k ∈ N. We show that if an infinite group G is either Abelian, or countable locally finite, or countable residually finite then, for each k ∈ N, G can be partitioned in two not k-prethick subsets.
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| first_indexed | 2025-12-07T20:12:59Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152243 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T20:12:59Z |
| publishDate | 2012 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Protasov, I.V. Slobodianiuk, S. 2019-06-09T06:10:55Z 2019-06-09T06:10:55Z 2012 Prethick subsets in partitions of groups / I.V. Protasov, S. Slobodianiuk // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 267–275. — Бібліогр.: 18 назв. — англ. 1726-3255 2010 MSC:05B40, 20A05. https://nasplib.isofts.kiev.ua/handle/123456789/152243 A subset S of a group G is called thick if, for any finite subset F of G, there exists g ∈ G such that Fg ⊆ S, and k-prethick, k ∈ N if there exists a subset K of G such that |K| = k and KS is thick. For every finite partition P of G, at least one cell of P is k-prethick for some k ∈ N. We show that if an infinite group G is either Abelian, or countable locally finite, or countable residually finite then, for each k ∈ N, G can be partitioned in two not k-prethick subsets. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Prethick subsets in partitions of groups Article published earlier |
| spellingShingle | Prethick subsets in partitions of groups Protasov, I.V. Slobodianiuk, S. |
| title | Prethick subsets in partitions of groups |
| title_full | Prethick subsets in partitions of groups |
| title_fullStr | Prethick subsets in partitions of groups |
| title_full_unstemmed | Prethick subsets in partitions of groups |
| title_short | Prethick subsets in partitions of groups |
| title_sort | prethick subsets in partitions of groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152243 |
| work_keys_str_mv | AT protasoviv prethicksubsetsinpartitionsofgroups AT slobodianiuks prethicksubsetsinpartitionsofgroups |