Partitions of groups into thin subsets
Let \(G\) be an infinite group with the identity \(e\), \(\kappa\) be an infinite cardinal \(\leqslant |G|\). A subset \(A\subset G\) is called \(\kappa\)-thin if \(|gA\cap A|\leqslant\kappa\) for every \(g\in G\setminus\{e\}\). We calculate the minimal cardinal \(\mu(G,\kappa)\) such that \(G\) can...
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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua:article-11022018-04-04T09:24:09Z Partitions of groups into thin subsets Protasov, Igor k-thin subsets of a group, partition of a group 03E75, 20F99, 20K99 Let \(G\) be an infinite group with the identity \(e\), \(\kappa\) be an infinite cardinal \(\leqslant |G|\). A subset \(A\subset G\) is called \(\kappa\)-thin if \(|gA\cap A|\leqslant\kappa\) for every \(g\in G\setminus\{e\}\). We calculate the minimal cardinal \(\mu(G,\kappa)\) such that \(G\) can be partitioned in \(\mu(G,\kappa)\) \(\kappa\)-thin subsets. In particular, we show that the statement \(\mu(\mathbb{R},\aleph_0)=\aleph_0\) is equivalent to the Continuum Hypothesis. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1102 Algebra and Discrete Mathematics; Vol 11, No 2 (2011) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1102/601 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2018-04-04T09:24:09Z |
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OJS |
| language |
English |
| topic |
k-thin subsets of a group partition of a group 03E75 20F99 20K99 |
| spellingShingle |
k-thin subsets of a group partition of a group 03E75 20F99 20K99 Protasov, Igor Partitions of groups into thin subsets |
| topic_facet |
k-thin subsets of a group partition of a group 03E75 20F99 20K99 |
| format |
Article |
| author |
Protasov, Igor |
| author_facet |
Protasov, Igor |
| author_sort |
Protasov, Igor |
| title |
Partitions of groups into thin subsets |
| 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 |
| description |
Let \(G\) be an infinite group with the identity \(e\), \(\kappa\) be an infinite cardinal \(\leqslant |G|\). A subset \(A\subset G\) is called \(\kappa\)-thin if \(|gA\cap A|\leqslant\kappa\) for every \(g\in G\setminus\{e\}\). We calculate the minimal cardinal \(\mu(G,\kappa)\) such that \(G\) can be partitioned in \(\mu(G,\kappa)\) \(\kappa\)-thin subsets. In particular, we show that the statement \(\mu(\mathbb{R},\aleph_0)=\aleph_0\) is equivalent to the Continuum Hypothesis. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1102 |
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AT protasovigor partitionsofgroupsintothinsubsets |
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2025-07-17T10:36:03Z |
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2025-07-17T10:36:03Z |
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1837890078372790272 |