Partitions of groups into sparse subsets

• Date: 2018
• Main Author: Protasov, Igor
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: partition of a group; sparse subset of a group; 03E75; 20F99; 20K99
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/695
• Journal Title: Algebra and Discrete Mathematics

A subset \(A\) of a group \(G\) is called sparse if, for every infinite subset \(X\) of \(G\), there exists a finite subset \(F\subset X\), such that \(\bigcap_{x\in F} xA\) is finite. We denote by \(\eta(G)\) the minimal cardinal such that \(G\) can be partitioned in \(\eta(G)\) sparse subsets. If...