RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

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

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)
References: PDF file   HTML file

Bibliographic databases:
MSC: 03E75, 20F99, 20K99
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} 

 SHARE:

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
2. Igor Protasov, Sergiy Slobodianiuk, “Prethick subsets in partitions of groups”, Algebra Discrete Math., 14:2 (2012), 267–275
3. Protasov I.V., “Thin Subsets of Topological Groups”, Topology Appl., 160:10 (2013), 1083–1087
4. Protasov I.V., Slobodyanyuk S., “Thin Subsets of Groups”, Ukr. Math. J., 65:9 (2014), 1384–1393
5. Banakh T.O. Protasov I.V. Slobodianiuk S.V., “Scattered Subsets of Groups”, Ukr. Math. J., 67:3 (2015), 347–356
6. Protasov I. Slobodianiuk S., “Partitions of Groups”, Adv. Appl. Discret. Math., 15:1 (2015), 33–60
•  Number of views: This page: 158 Full text: 61 References: 31 First page: 1