Zero-sum subsets of decomposable sets in Abelian groups

• Published in: Algebra and Discrete Mathematics
• Date: 2020
• Main Authors: Banakh, T., Ravsky, A.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188550
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Zero-sum subsets of decomposable sets in Abelian groups / T. Banakh, A. Ravsky // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 15–25. — Бібліогр.: 3 назв. — англ.

A subset D of an abelian group is decomposable if ∅ ≠ D ⊂ 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 ⊂ D with ∑Z = 0.