Densities, submeasures and partitions of groups

• Published in: Algebra and Discrete Mathematics
• Date: 2014
• Main Authors: Banakh, T., Protasov, I., Slobodianiuk, S.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2014
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/153328
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Densities, submeasures and partitions of groups / T. Banakh, I. Protasov, S. Slobodianiuk // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 2. — С. 193–221. — Бібліогр.: 25 назв. — англ.

In 1995 in Kourovka notebook the second author asked the following problem: is it true that for each partition G=A₁ ∪ ⋯ ∪ An of a group G there is a cell Ai of the partition such that G = FAiA⁻¹i for some set F ⊂ G of cardinality |F |≤ n? In this paper we survey several partial solutions of this pro...