Thin systems of generators of groups

• Date: 2018
• Main Author: Lutsenko, Ievgen
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: small; P-small; \(k\)-thin subsets of groups; 20F05; 20F99
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/634
• Journal Title: Algebra and Discrete Mathematics

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...