Densities, submeasures and partitions of groups

• Date: 2018
• Main Authors: Banakh, Taras, Protasov, Igor, Slobodianiuk, Sergiy
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: partition of a group; density; submeasure; amenable group; 05E15; 05D10; 28C10
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1031
• Journal Title: Algebra and Discrete Mathematics

In 1995 in Kourovka notebook the second author asked the following problem:  is it true that for each partition \(G=A_1\cup\dots\cup A_n\) of a group \(G\) there is a cell \(A_i\) of the partition such that \(G=FA_iA_i^{-1}\) for some set \(F\subset G\) of cardinality \(|F|\le n\)?  In this paper we...