Partitions of groups into sparse subsets
A subset A of a group G is called sparse if, for every infinite subset X of G, there exists a finite subset F ⊂ X, such that ∩x∈FxA is finite. We denote by η(G) the minimal cardinal such that G can be partitioned in η(G) sparse subsets. If |G| > (κ+)א0 then η(G) > κ, if |G| ≤ κ+ then η(G) ≤ κ....
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2012 |
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| Format: | Article |
| 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/123456789/152190 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Partitions of groups into sparse subsets / I. Protasov // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 107–110. — Бібліогр.: 7 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862634814990974976 |
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| author | Protasov, I. |
| author_facet | Protasov, I. |
| citation_txt | Partitions of groups into sparse subsets / I. Protasov // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 107–110. — Бібліогр.: 7 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | A subset A of a group G is called sparse if, for every infinite subset X of G, there exists a finite subset F ⊂ X, such that ∩x∈FxA is finite. We denote by η(G) the minimal cardinal such that G can be partitioned in η(G) sparse subsets. If |G| > (κ+)א0 then η(G) > κ, if |G| ≤ κ+ then η(G) ≤ κ. We show also that cov(A) ≥ cf|G| for each sparse subset A of an infinite group G, where cov(A) = min{|X| : G = X A}.
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| first_indexed | 2025-11-30T16:38:26Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152190 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-30T16:38:26Z |
| publishDate | 2012 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Protasov, I. 2019-06-08T11:08:38Z 2019-06-08T11:08:38Z 2012 Partitions of groups into sparse subsets / I. Protasov // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 107–110. — Бібліогр.: 7 назв. — англ. 1726-3255 2010 Mathematics Subject Classification: 03E75, 20F99, 20K99. https://nasplib.isofts.kiev.ua/handle/123456789/152190 A subset A of a group G is called sparse if, for every infinite subset X of G, there exists a finite subset F ⊂ X, such that ∩x∈FxA is finite. We denote by η(G) the minimal cardinal such that G can be partitioned in η(G) sparse subsets. If |G| > (κ+)א0 then η(G) > κ, if |G| ≤ κ+ then η(G) ≤ κ. We show also that cov(A) ≥ cf|G| for each sparse subset A of an infinite group G, where cov(A) = min{|X| : G = X A}. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Partitions of groups into sparse subsets Article published earlier |
| spellingShingle | Partitions of groups into sparse subsets Protasov, I. |
| title | Partitions of groups into sparse subsets |
| title_full | Partitions of groups into sparse subsets |
| title_fullStr | Partitions of groups into sparse subsets |
| title_full_unstemmed | Partitions of groups into sparse subsets |
| title_short | Partitions of groups into sparse subsets |
| title_sort | partitions of groups into sparse subsets |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152190 |
| work_keys_str_mv | AT protasovi partitionsofgroupsintosparsesubsets |