Partitions of groups into thin subsets

Let G be an infinite group with the identity e, κ be an infinite cardinal ≤|G|. A subset A⊂G is called κ-thin if |gA∩A|≤κ for every g∈G∖{e}. We calculate the minimal cardinal μ(G,κ) such that G can be partitioned in μ(G,κ) κ-thin subsets. In particular, we show that the statement μ(R,ℵ₀)=ℵ₀ is equiv...

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Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2011
1. Verfasser: Protasov, I.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2011
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/154850
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Zitieren:Partitions of groups into thin subsets / I. Protasov // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 2. — С. 78–81. — Бібліогр.: 6 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-154850
record_format dspace
spelling Protasov, I.
2019-06-16T05:44:39Z
2019-06-16T05:44:39Z
2011
Partitions of groups into thin subsets / I. Protasov // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 2. — С. 78–81. — Бібліогр.: 6 назв. — англ.
1726-3255
2000 Mathematics Subject Classification:03E75, 20F99, 20K99
https://nasplib.isofts.kiev.ua/handle/123456789/154850
Let G be an infinite group with the identity e, κ be an infinite cardinal ≤|G|. A subset A⊂G is called κ-thin if |gA∩A|≤κ for every g∈G∖{e}. We calculate the minimal cardinal μ(G,κ) such that G can be partitioned in μ(G,κ) κ-thin subsets. In particular, we show that the statement μ(R,ℵ₀)=ℵ₀ is equivalent to the Continuum Hypothesis.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Partitions of groups into thin subsets
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Partitions of groups into thin subsets
spellingShingle Partitions of groups into thin subsets
Protasov, I.
title_short Partitions of groups into thin subsets
title_full Partitions of groups into thin subsets
title_fullStr Partitions of groups into thin subsets
title_full_unstemmed Partitions of groups into thin subsets
title_sort partitions of groups into thin subsets
author Protasov, I.
author_facet Protasov, I.
publishDate 2011
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
description Let G be an infinite group with the identity e, κ be an infinite cardinal ≤|G|. A subset A⊂G is called κ-thin if |gA∩A|≤κ for every g∈G∖{e}. We calculate the minimal cardinal μ(G,κ) such that G can be partitioned in μ(G,κ) κ-thin subsets. In particular, we show that the statement μ(R,ℵ₀)=ℵ₀ is equivalent to the Continuum Hypothesis.
issn 1726-3255
url https://nasplib.isofts.kiev.ua/handle/123456789/154850
citation_txt Partitions of groups into thin subsets / I. Protasov // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 2. — С. 78–81. — Бібліогр.: 6 назв. — англ.
work_keys_str_mv AT protasovi partitionsofgroupsintothinsubsets
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last_indexed 2025-12-07T20:45:26Z
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