Partitions of groups into sparse subsets

dc.contributor.author	Protasov, I.
dc.date.accessioned	2019-06-08T11:08:38Z
dc.date.available	2019-06-08T11:08:38Z
dc.date.issued	2012
dc.identifier.citation	Partitions of groups into sparse subsets / I. Protasov // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 107–110. — Бібліогр.: 7 назв. — англ.	uk_UA
dc.identifier.issn	1726-3255
dc.identifier.other	2010 Mathematics Subject Classification: 03E75, 20F99, 20K99.
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/152190
dc.description.abstract	A subset A of a group G is called sparse if, for every infinite subset X of G, there exists a finite subset F ⊂ X, such that ∩x∈FxA is finite. We denote by η(G) the minimal cardinal such that G can be partitioned in η(G) sparse subsets. If \|G\| > (κ+)א0 then η(G) > κ, if \|G\| ≤ κ+ then η(G) ≤ κ. We show also that cov(A) ≥ cf\|G\| for each sparse subset A of an infinite group G, where cov(A) = min{\|X\| : G = X A}.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут прикладної математики і механіки НАН України	uk_UA
dc.relation.ispartof	Algebra and Discrete Mathematics
dc.title	Partitions of groups into sparse subsets	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA