Zero-sum subsets of decomposable sets in Abelian groups

• Дата: 2020
• Автори: Banakh, T., Ravsky, A.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Lugansk National Taras Shevchenko University 2020
• Теми: decomposable set; abelian group; sum-set; 05E15
• Онлайн доступ: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1494
• Назва журналу: Algebra and Discrete Mathematics

A subset \(D\) of an abelian group is decomposable if \( \emptyset\ne D\subset D+D\). In the paper we give partial answers to an open problem asking whether every finite decomposable subset \(D\) of an abelian group contains a non-empty subset \(Z\subset D\) with \(\sum Z=0\). For every \(n\in\mathb...