Partitions of groups into thin subsets
Let G be an infinite group with the identity e, κ be an infinite cardinal ≤|G|. A subset A⊂G is called κ-thin if |gA∩A|≤κ for every g∈G∖{e}. We calculate the minimal cardinal μ(G,κ) such that G can be partitioned in μ(G,κ) κ-thin subsets. In particular, we show that the statement μ(R,ℵ₀)=ℵ₀ is equiv...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2011
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| Zitieren: | Partitions of groups into thin subsets / I. Protasov // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 2. — С. 78–81. — Бібліогр.: 6 назв. — англ. |
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Protasov, I. 2019-06-16T05:44:39Z 2019-06-16T05:44:39Z 2011 Partitions of groups into thin subsets / I. Protasov // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 2. — С. 78–81. — Бібліогр.: 6 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:03E75, 20F99, 20K99 https://nasplib.isofts.kiev.ua/handle/123456789/154850 Let G be an infinite group with the identity e, κ be an infinite cardinal ≤|G|. A subset A⊂G is called κ-thin if |gA∩A|≤κ for every g∈G∖{e}. We calculate the minimal cardinal μ(G,κ) such that G can be partitioned in μ(G,κ) κ-thin subsets. In particular, we show that the statement μ(R,ℵ₀)=ℵ₀ is equivalent to the Continuum Hypothesis. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Partitions of groups into thin subsets Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Partitions of groups into thin subsets |
| spellingShingle |
Partitions of groups into thin subsets Protasov, I. |
| title_short |
Partitions of groups into thin subsets |
| title_full |
Partitions of groups into thin subsets |
| title_fullStr |
Partitions of groups into thin subsets |
| title_full_unstemmed |
Partitions of groups into thin subsets |
| title_sort |
partitions of groups into thin subsets |
| author |
Protasov, I. |
| author_facet |
Protasov, I. |
| publishDate |
2011 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
Let G be an infinite group with the identity e, κ be an infinite cardinal ≤|G|. A subset A⊂G is called κ-thin if |gA∩A|≤κ for every g∈G∖{e}. We calculate the minimal cardinal μ(G,κ) such that G can be partitioned in μ(G,κ) κ-thin subsets. In particular, we show that the statement μ(R,ℵ₀)=ℵ₀ is equivalent to the Continuum Hypothesis.
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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/154850 |
| citation_txt |
Partitions of groups into thin subsets / I. Protasov // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 2. — С. 78–81. — Бібліогр.: 6 назв. — англ. |
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2025-12-07T20:45:26Z |
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2025-12-07T20:45:26Z |
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1850883782815514624 |