Partitions of groups into sparse subsets

• Datum: 2018
• 1. Verfasser: Protasov, Igor
• Format: Artikel
• Sprache: English
• Veröffentlicht: Lugansk National Taras Shevchenko University 2018
• Schlagworte: partition of a group; sparse subset of a group; 03E75; 20F99; 20K99
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/695
• Назва журналу: 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...