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Algebra Discrete Math., 2012, Volume 14, Issue 2, Pages 267–275 (Mi adm98)  

This article is cited in 1 scientific paper (total in 1 paper)

RESEARCH ARTICLE

Prethick subsets in partitions of groups

Igor Protasov, Sergiy Slobodianiuk

Department of Cybernetics, Kyiv National University, Volodymirska 64, 01033, Kyiv, Ukraine

Abstract: A subset $S$ of a group $G$ is called thick if, for any finite subset $F$ of $G$, there exists $g\in G$ such that $Fg\subseteq S$, and $k$-prethick, $k\in \mathbb{N}$ if there exists a subset $K$ of $G$ such that $|K|=k$ and $KS$ is thick. For every finite partition $\mathcal{P}$ of $G$, at least one cell of $\mathcal{P}$ is $k$-prethick for some $k\in \mathbb{N}$. We show that if an infinite group $G$ is either Abelian, or countable locally finite, or countable residually finite then, for each $k\in \mathbb{N}$, $G$ can be partitioned in two not $k$-prethick subsets.

Keywords: thick and $k$-prethick subsets of groups, $k$-meager partition of a group.

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Bibliographic databases:
MSC: 05B40, 20A05
Received: 11.09.2012
Accepted:11.09.2012
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Citation: Igor Protasov, Sergiy Slobodianiuk, “Prethick subsets in partitions of groups”, Algebra Discrete Math., 14:2 (2012), 267–275

Citation in format AMSBIB
\Bibitem{ProSlo12}
\by Igor~Protasov, Sergiy~Slobodianiuk
\paper Prethick subsets in partitions of groups
\jour Algebra Discrete Math.
\yr 2012
\vol 14
\issue 2
\pages 267--275
\mathnet{http://mi.mathnet.ru/adm98}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3099974}
\zmath{https://zbmath.org/?q=an:1288.20056}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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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