Zero-sum subsets of decomposable sets in Abelian groups

• Date: 2020
• Main Authors: Banakh, T., Ravsky, A.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2020
• Subjects: decomposable set; abelian group; sum-set; 05E15
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1494
• Journal Title: 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...