TY - JOUR
AU - I. V. Protasov
AU - S. V. Slobodianiuk
PY - 2013/09/25
Y2 - 2023/03/26
TI - Thin Subsets of Groups
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 65
IS - 9
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2505
AB - 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 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.
ER -