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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2012 |
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| Language: | English |
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Інститут прикладної математики і механіки НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152243 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Prethick subsets in partitions of groups |
| spellingShingle |
Prethick subsets in partitions of groups Protasov, I.V. Slobodianiuk, S. |
| title_short |
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_sort |
prethick subsets in partitions of groups |
| author |
Protasov, I.V. Slobodianiuk, S. |
| author_facet |
Protasov, I.V. Slobodianiuk, S. |
| publishDate |
2012 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/152243 |
| 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. |
| work_keys_str_mv |
AT protasoviv prethicksubsetsinpartitionsofgroups AT slobodianiuks prethicksubsetsinpartitionsofgroups |
| first_indexed |
2025-12-07T20:12:59Z |
| last_indexed |
2025-12-07T20:12:59Z |
| _version_ |
1850881741800079360 |