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

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.

Full text: PDF file (176 kB)
References: PDF file   HTML file

Bibliographic databases:
MSC: 05B40, 20A05
Accepted:11.09.2012
Language:

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}