Ukrainian Mathematical Journal

, Volume 65, Issue 9, pp 1384–1393

Thin Subsets of Groups

  • I. V. Protasov
  • S. Slobodyanyuk

DOI: 10.1007/s11253-014-0866-2

Cite this article as:
Protasov, I.V. & Slobodyanyuk, S. Ukr Math J (2014) 65: 1384. doi:10.1007/s11253-014-0866-2

For a group G and a natural number m; a subset A of G is called m-thin if, for each finite subset F of G; there exists a finite subset K of G such that |FgA| ≤ m for all gG \ K: We show that each m-thin subset of an Abelian group G of cardinality ℵn; n = 0, 1,… can be split into ≤ mn+1 1-thin subsets. On the other hand, we construct a group G of cardinality ℵω and select a 2-thin subset of G which cannot be split into finitely many 1-thin subsets.

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • I. V. Protasov
    • 1
  • S. Slobodyanyuk
    • 1
  1. 1.Shevchenko Kyiv National UniversityKyivUkraine

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