Partitions of groups into sparse subsets

• Datum: 2012
• 1. Verfasser: Protasov, I.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2012
• Schriftenreihe: Algebra and Discrete Mathematics
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/152190
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Partitions of groups into sparse subsets / I. Protasov // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 107–110. — Бібліогр.: 7 назв. — англ.

A subset A of a group G is called sparse if, for every infinite subset X of G, there exists a finite subset F ⊂ X, such that ∩x∈FxA is finite. We denote by η(G) the minimal cardinal such that G can be partitioned in η(G) sparse subsets. If |G| > (κ+)א0 then η(G) > κ, if |G| ≤ κ+ then η(G) ≤ κ....