Thin Subsets of Groups

  • I. V. Protasov Kyiv Nat. Taras Shevchenko Univ.
  • S. V. Slobodianiuk

Abstract

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 |F g A| ≤ m for all gG \ K: We show that each m-thin subset of an Abelian group G of cardinality ℵ n ; n = 0, 1,… can be split into ≤ m n+1 1-thin subsets. On the other hand, we construct a group G of cardinality ℵ ω and select a 2-thin subset of G which cannot be split into finitely many 1-thin subsets.
Published
25.09.2013
How to Cite
ProtasovI. V., and SlobodianiukS. V. “Thin Subsets of Groups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 9, Sept. 2013, pp. 1245–1253, http://umj.imath.kiev.ua/index.php/umj/article/view/2505.
Section
Research articles