Thin systems of generators of groups
A subset \(T\) of a group \(G\) with the identity \(e\) is called \(k\)-thin (\(k\in\mathbb{N}\)) if \(|A\cap gA|\leqslant k\), \(|A\cap Ag|\leqslant k\) for every \(g\in G\), \(g\ne e\). We show that every infinite group \(G\) can be generated by some 2-thin subset. Moreover, if \(G\) is either Ab...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/634 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-6342018-04-04T09:11:25Z Thin systems of generators of groups Lutsenko, Ievgen small, P-small, \(k\)-thin subsets of groups 20F05, 20F99 A subset \(T\) of a group \(G\) with the identity \(e\) is called \(k\)-thin (\(k\in\mathbb{N}\)) if \(|A\cap gA|\leqslant k\), \(|A\cap Ag|\leqslant k\) for every \(g\in G\), \(g\ne e\). We show that every infinite group \(G\) can be generated by some 2-thin subset. Moreover, if \(G\) is either Abelian or a torsion group without elements of order 2, then there exists a 1-thin system of generators of \(G\). For every infinite group \(G\), there exist a 2-thin subset \(X\) such that \(G=XX^{-1}\cup X^{-1}X\), and a 4-thin subset \(Y\) such that \(G=YY^{-1}\). 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/634 Algebra and Discrete Mathematics; Vol 9, No 2 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/634/168 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
small P-small \(k\)-thin subsets of groups 20F05 20F99 |
| spellingShingle |
small P-small \(k\)-thin subsets of groups 20F05 20F99 Lutsenko, Ievgen Thin systems of generators of groups |
| topic_facet |
small P-small \(k\)-thin subsets of groups 20F05 20F99 |
| format |
Article |
| author |
Lutsenko, Ievgen |
| author_facet |
Lutsenko, Ievgen |
| author_sort |
Lutsenko, Ievgen |
| title |
Thin systems of generators of groups |
| title_short |
Thin systems of generators of groups |
| title_full |
Thin systems of generators of groups |
| title_fullStr |
Thin systems of generators of groups |
| title_full_unstemmed |
Thin systems of generators of groups |
| title_sort |
thin systems of generators of groups |
| description |
A subset \(T\) of a group \(G\) with the identity \(e\) is called \(k\)-thin (\(k\in\mathbb{N}\)) if \(|A\cap gA|\leqslant k\), \(|A\cap Ag|\leqslant k\) for every \(g\in G\), \(g\ne e\). We show that every infinite group \(G\) can be generated by some 2-thin subset. Moreover, if \(G\) is either Abelian or a torsion group without elements of order 2, then there exists a 1-thin system of generators of \(G\). For every infinite group \(G\), there exist a 2-thin subset \(X\) such that \(G=XX^{-1}\cup X^{-1}X\), and a 4-thin subset \(Y\) such that \(G=YY^{-1}\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/634 |
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AT lutsenkoievgen thinsystemsofgeneratorsofgroups |
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2024-04-12T06:27:27Z |
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2024-04-12T06:27:27Z |
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1796109251441065984 |