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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra Discrete Math., 2012, Volume 13, Issue 1, Pages 107–110 (Mi adm68)  

This article is cited in 2 scientific papers (total in 2 papers)

RESEARCH ARTICLE

Partitions of groups into sparse subsets

Igor Protasov

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

Abstract: A subset $A$ of a group $G$ is called sparse if, for every infinite subset $X$ of $G$, there exists a finite subset $F\subset X$, such that $\bigcap_{x\in F} xA$ is finite. We denote by $\eta(G)$ the minimal cardinal such that $G$ can be partitioned in $\eta(G)$ sparse subsets. If $|G| > (\kappa^+)^{\aleph_0}$ then $\eta(G) > \kappa$, if $|G|\leqslant \kappa^+$ then $\eta(G) \leqslant \kappa$. We show also that $cov(A) \geqslant cf|G|$ for each sparse subset $A$ of an infinite group $G$, where $cov(A)=\min\{|X|: G = XA\}$.

Keywords: partition of a group, sparse subset of a group.

Full text: PDF file (180 kB)
References: PDF file   HTML file

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

Citation: Igor Protasov, “Partitions of groups into sparse subsets”, Algebra Discrete Math., 13:1 (2012), 107–110

Citation in format AMSBIB
\Bibitem{Pro12}
\by Igor~Protasov
\paper Partitions of groups into sparse subsets
\jour Algebra Discrete Math.
\yr 2012
\vol 13
\issue 1
\pages 107--110
\mathnet{http://mi.mathnet.ru/adm68}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2963828}
\zmath{https://zbmath.org/?q=an:1258.20036}


Linking options:
  • http://mi.mathnet.ru/eng/adm68
  • http://mi.mathnet.ru/eng/adm/v13/i1/p107

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. 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
    2. Protasov I. Slobodianiuk S., “Partitions of Groups”, Adv. Appl. Discret. Math., 15:1 (2015), 33–60  mathscinet  zmath  isi
  • Algebra and Discrete Mathematics
    Number of views:
    This page:152
    Full text:62
    References:20
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020