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 |
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| Дата: | 2012 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| 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| Резюме: | 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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| ISSN: | 1726-3255 |