Prethick subsets in partitions of groups

• Date: 2018
• Main Authors: Protasov, Igor, Slobodianiuk, Sergiy
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: thick and \(k\)-prethick subsets of groups; \(k\)-meager partition of a group; 05B40; 20A05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/725
• Journal Title: Algebra and Discrete Mathematics

A subset \(S\) of a group \(G\) is called thick if, for any finite subset \(F\) of \(G\), there exists \(g\in G\) such that \(Fg\subseteq S\), and \(k\)-prethick, \(k\in \mathbb{N}\) if there exists a subset \(K\) of \(G\) such that \(|K|=k\) and \(KS\) is thick. For every finite partition \(\mathca...