Thin Subsets of Groups

• Date: 2013
• Main Authors: Protasov, I. V., Slobodianiuk, S. V., Протасов, І. В., Слободянюк, С. В.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2013
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2505
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 g ∈ G \ 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...