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Algebra and Discrete Mathematics, 2011, Volume 11, Issue 2, Pages 78–81
(Mi adm12)
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This article is cited in 6 scientific papers (total in 6 papers)
RESEARCH ARTICLE
Partitions of groups into thin subsets
Igor Protasov Department of Cybernetics, Kyiv National University, Volodymyrska 64, 01033, Kyiv, Ukraine
Abstract:
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.
Keywords:
$\kappa$-thin subsets of a group, partition of a group.
Received: 13.03.2011 Revised: 13.03.2011
Citation:
Igor Protasov, “Partitions of groups into thin subsets”, Algebra Discrete Math., 11:2 (2011), 78–81
Linking options:
https://www.mathnet.ru/eng/adm12 https://www.mathnet.ru/eng/adm/v11/i2/p78
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Abstract page: | 268 | Full-text PDF : | 87 | References: | 45 | First page: | 1 |
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