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 \(g\in G\) such that \(Fg\subseteq S\), and \(k\)-prethick, \(k\in \mathbb{N}\) if there exists a subset \(K\) of \(G\) such that \(|K|=k\) and \(KS\) is thick. For every finite partition \(\mathca...
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| Дата: | 2018 |
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| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-7252018-04-04T10:03:23Z Prethick subsets in partitions of groups Protasov, Igor Slobodianiuk, Sergiy thick and \(k\)-prethick subsets of groups, \(k\)-meager partition of a group 05B40, 20A05 A subset \(S\) of a group \(G\) is called thick if, for any finite subset \(F\) of \(G\), there exists \(g\in G\) such that \(Fg\subseteq S\), and \(k\)-prethick, \(k\in \mathbb{N}\) if there exists a subset \(K\) of \(G\) such that \(|K|=k\) and \(KS\) is thick. For every finite partition \(\mathcal{P}\) of \(G\), at least one cell of \(\mathcal{P}\) is \(k\)-prethick for some \(k\in \mathbb{N}\). We show that if an infinite group \(G\) is either Abelian, or countable locally finite, or countable residually finite then, for each \(k\in \mathbb{N}\), \(G\) can be partitioned in two not \(k\)-prethick subsets. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/725 Algebra and Discrete Mathematics; Vol 14, No 2 (2012) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/725/257 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
thick and \(k\)-prethick subsets of groups \(k\)-meager partition of a group 05B40 20A05 |
| spellingShingle |
thick and \(k\)-prethick subsets of groups \(k\)-meager partition of a group 05B40 20A05 Protasov, Igor Slobodianiuk, Sergiy Prethick subsets in partitions of groups |
| topic_facet |
thick and \(k\)-prethick subsets of groups \(k\)-meager partition of a group 05B40 20A05 |
| format |
Article |
| author |
Protasov, Igor Slobodianiuk, Sergiy |
| author_facet |
Protasov, Igor Slobodianiuk, Sergiy |
| author_sort |
Protasov, Igor |
| title |
Prethick subsets in partitions of groups |
| title_short |
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_sort |
prethick subsets in partitions of groups |
| description |
A subset \(S\) of a group \(G\) is called thick if, for any finite subset \(F\) of \(G\), there exists \(g\in G\) such that \(Fg\subseteq S\), and \(k\)-prethick, \(k\in \mathbb{N}\) if there exists a subset \(K\) of \(G\) such that \(|K|=k\) and \(KS\) is thick. For every finite partition \(\mathcal{P}\) of \(G\), at least one cell of \(\mathcal{P}\) is \(k\)-prethick for some \(k\in \mathbb{N}\). We show that if an infinite group \(G\) is either Abelian, or countable locally finite, or countable residually finite then, for each \(k\in \mathbb{N}\), \(G\) can be partitioned in two not \(k\)-prethick subsets. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/725 |
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2024-04-12T06:26:16Z |
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2024-04-12T06:26:16Z |
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