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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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Інститут прикладної математики і механіки НАН України
2012
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| Series: | Algebra and Discrete Mathematics |
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irk-123456789-1521902019-06-09T01:25:00Z Partitions of groups into sparse subsets Protasov, I. 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}. 2012 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/152190 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| language |
English |
| 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}. |
| format |
Article |
| author |
Protasov, I. |
| spellingShingle |
Protasov, I. Partitions of groups into sparse subsets Algebra and Discrete Mathematics |
| author_facet |
Protasov, I. |
| author_sort |
Protasov, I. |
| title |
Partitions of groups into sparse subsets |
| title_short |
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_sort |
partitions of groups into sparse subsets |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152190 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT protasovi partitionsofgroupsintosparsesubsets |
| first_indexed |
2023-05-20T17:37:41Z |
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2023-05-20T17:37:41Z |
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1796153724380381184 |