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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W. / Wilson, John S.

Managing Editor: Khukhro, Evgenii I. / Kramer, Linus

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In This Section
Volume 20, Issue 1 (Jan 2017)

Issues

A note on Factoring groups into dense subsets

Igor Protasov
  • Department of Cybernetics, Kyiv University, Volodymyrska 64, 01033, Kyiv, Ukraine
  • Email:
/ Serhii Slobodianiuk
  • Department of Mechanics and Mathematics, Kyiv University, Volodymyrska 64, 01033, Kyiv, Ukraine
  • Email:
Published Online: 2016-05-18 | DOI: https://doi.org/10.1515/jgth-2016-0021

Abstract

Let G be a group of cardinality κ>0 endowed with a topology 𝒯 such that |U|=κ for every non-empty U𝒯 and 𝒯 has a base of cardinality κ. We prove that G can be factorized G=AB (i.e. each gG has a unique representation g=ab, aA, bB) into dense subsets A, B, |A|=|B|=κ. We do not know if this statement holds for κ=0 even if G is a topological group.

References

  • [1]

    Ceder J., On maximally resolvable spaces, Fund. Math. 55 (1964), 87–93.

  • [2]

    Comfort W. and van Mill J., Group with only resolvable group topologies, Proc. Amer. Math. Soc. 120 (1993), 687–696.

  • [3]

    Filali M. and Protasov I., Ultrafilters and Topologies on Groups, Math. Stud. Monogr. Ser. 13, VNTL, Lviv, 2010.

  • [4]

    Hewitt E., A problem of set-theoretic topology, Duke Math. J. 10 (1943), 309–333.

  • [5]

    Malykhin V., Extremally disconnected and similar groups, Soviet Math. Dokl. 16 (1975), 21–25. .

  • [6]

    Protasov I., Irresolvable topologies on groups, Ukr. Math. J. 50 (1998), 1879–1887.

  • [7]

    Protasov I., Box resolvability, preprint 2015, http://arxiv.org/abs/1511.01046; to appear in Topology Appl.

  • [8]

    Shelah S., Proper Forcing, Lecture Notes in Math. 940, Springer, Berlin, 1982.

  • [9]

    Szabó S. and Sands A., Factoring Groups into Subsets, CRC Press, Boca Raton, 2009.

  • [10]

    Zelenyuk E., On partitions of groups into dense subsets, Topology Appl. 126 (2002), 327–339.

  • [11]

    Zelenyuk E., Partitions and sums with inverse in Abelian groups, J. Combin. Theory Ser. A 115 (2008), 331–339.

About the article


Received: 2016-02-14

Revised: 2016-04-29

Published Online: 2016-05-18

Published in Print: 2017-01-01



Citation Information: Journal of Group Theory, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgth-2016-0021. Export Citation

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