Prethick subsets in partitions of groups

A subset S of a group G is called thick if, for any finite subset F of G, there exists g ∈ G such that Fg ⊆ S, and k-prethick, k ∈ N if there exists a subset K of G such that |K| = k and KS is thick. For every finite partition P of G, at least one cell of P is k-prethick for some k ∈ N. We show that...

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Опубліковано в: :Algebra and Discrete Mathematics
Дата:2012
Автори: Protasov, I.V., Slobodianiuk, S.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут прикладної математики і механіки НАН України 2012
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/152243
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Prethick subsets in partitions of groups / I.V. Protasov, S. Slobodianiuk // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 267–275. — Бібліогр.: 18 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Protasov, I.V.
Slobodianiuk, S.
author_facet Protasov, I.V.
Slobodianiuk, S.
citation_txt Prethick subsets in partitions of groups / I.V. Protasov, S. Slobodianiuk // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 267–275. — Бібліогр.: 18 назв. — англ.
collection DSpace DC
container_title Algebra and Discrete Mathematics
description A subset S of a group G is called thick if, for any finite subset F of G, there exists g ∈ G such that Fg ⊆ S, and k-prethick, k ∈ N if there exists a subset K of G such that |K| = k and KS is thick. For every finite partition P of G, at least one cell of P is k-prethick for some k ∈ N. We show that if an infinite group G is either Abelian, or countable locally finite, or countable residually finite then, for each k ∈ N, G can be partitioned in two not k-prethick subsets.
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1726-3255
language English
last_indexed 2025-12-07T20:12:59Z
publishDate 2012
publisher Інститут прикладної математики і механіки НАН України
record_format dspace
spelling Protasov, I.V.
Slobodianiuk, S.
2019-06-09T06:10:55Z
2019-06-09T06:10:55Z
2012
Prethick subsets in partitions of groups / I.V. Protasov, S. Slobodianiuk // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 267–275. — Бібліогр.: 18 назв. — англ.
1726-3255
2010 MSC:05B40, 20A05.
https://nasplib.isofts.kiev.ua/handle/123456789/152243
A subset S of a group G is called thick if, for any finite subset F of G, there exists g ∈ G such that Fg ⊆ S, and k-prethick, k ∈ N if there exists a subset K of G such that |K| = k and KS is thick. For every finite partition P of G, at least one cell of P is k-prethick for some k ∈ N. We show that if an infinite group G is either Abelian, or countable locally finite, or countable residually finite then, for each k ∈ N, G can be partitioned in two not k-prethick subsets.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Prethick subsets in partitions of groups
Article
published earlier
spellingShingle Prethick subsets in partitions of groups
Protasov, I.V.
Slobodianiuk, S.
title Prethick subsets in partitions of groups
title_full Prethick subsets in partitions of groups
title_fullStr Prethick subsets in partitions of groups
title_full_unstemmed Prethick subsets in partitions of groups
title_short Prethick subsets in partitions of groups
title_sort prethick subsets in partitions of groups
url https://nasplib.isofts.kiev.ua/handle/123456789/152243
work_keys_str_mv AT protasoviv prethicksubsetsinpartitionsofgroups
AT slobodianiuks prethicksubsetsinpartitionsofgroups