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: | Englisch |
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Інститут прикладної математики і механіки НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/154850 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862746293462368256 |
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| author | Protasov, I. |
| author_facet | Protasov, I. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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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| first_indexed | 2025-12-07T20:45:26Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154850 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T20:45:26Z |
| publishDate | 2011 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Partitions of groups into thin subsets Protasov, I. |
| title | 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_short | Partitions of groups into thin subsets |
| title_sort | partitions of groups into thin subsets |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154850 |
| work_keys_str_mv | AT protasovi partitionsofgroupsintothinsubsets |