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Algebra Discrete Math., 2011, Volume 11, Issue 2, Pages 78–81 (Mi adm12)  

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.

Full text: PDF file (204 kB)
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Bibliographic databases:
MSC: 03E75, 20F99, 20K99
Received: 13.03.2011
Revised: 13.03.2011
Language:

Citation: Igor Protasov, “Partitions of groups into thin subsets”, Algebra Discrete Math., 11:2 (2011), 78–81

Citation in format AMSBIB
\Bibitem{Pro11}
\by Igor Protasov
\paper Partitions of groups into thin subsets
\jour Algebra Discrete Math.
\yr 2011
\vol 11
\issue 2
\pages 78--81
\mathnet{http://mi.mathnet.ru/adm12}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2858130}
\zmath{https://zbmath.org/?q=an:1257.20046}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Igor Protasov, “Partitions of groups into sparse subsets”, Algebra Discrete Math., 13:1 (2012), 107–110  mathnet  mathscinet  zmath
    2. Igor Protasov, Sergiy Slobodianiuk, “Prethick subsets in partitions of groups”, Algebra Discrete Math., 14:2 (2012), 267–275  mathnet  mathscinet  zmath
    3. Protasov I.V., “Thin Subsets of Topological Groups”, Topology Appl., 160:10 (2013), 1083–1087  crossref  mathscinet  zmath  isi  elib  scopus
    4. Protasov I.V., Slobodyanyuk S., “Thin Subsets of Groups”, Ukr. Math. J., 65:9 (2014), 1384–1393  crossref  mathscinet  zmath  isi  elib  scopus
    5. Banakh T.O. Protasov I.V. Slobodianiuk S.V., “Scattered Subsets of Groups”, Ukr. Math. J., 67:3 (2015), 347–356  crossref  mathscinet  zmath  isi  elib  scopus
    6. Protasov I. Slobodianiuk S., “Partitions of Groups”, Adv. Appl. Discret. Math., 15:1 (2015), 33–60  mathscinet  zmath  isi
  • Algebra and Discrete Mathematics
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