Prethick subsets in partitions of groups

• Published in: Algebra and Discrete Mathematics
• Date: 2012
• Main Authors: Protasov, I.V., Slobodianiuk, S.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2012
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/152243
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Prethick subsets in partitions of groups / I.V. Protasov, S. Slobodianiuk // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 267–275. — Бібліогр.: 18 назв. — англ.

A subset S of a group G is called thick if, for any finite subset F of G, there exists g ∈ G such that Fg ⊆ S, and k-prethick, k ∈ N if there exists a subset K of G such that |K| = k and KS is thick. For every finite partition P of G, at least one cell of P is k-prethick for some k ∈ N. We show that...