Partitions of groups into thin subsets

• Дата: 2018
• Автор: Protasov, Igor
• Формат: Стаття
• Мова: English
• Опубліковано: Lugansk National Taras Shevchenko University 2018
• Теми: k-thin subsets of a group; partition of a group; 03E75; 20F99; 20K99
• Онлайн доступ: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1102
• Назва журналу: Algebra and Discrete Mathematics

Let \(G\) be an infinite group with the identity \(e\), \(\kappa\) be an infinite cardinal \(\leqslant |G|\). A subset \(A\subset G\) is called \(\kappa\)-thin if \(|gA\cap A|\leqslant\kappa\) for every \(g\in G\setminus\{e\}\). We calculate the minimal cardinal \(\mu(G,\kappa)\) such that \(G\) can...