Thin systems of generators of groups

• Published in: Algebra and Discrete Mathematics
• Date: 2010
• Main Author: Lutsenko, I.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/154507
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Thin systems of generators of groups / I. Lutsenko // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 106–112. — Бібліогр.: 6 назв. — англ.

A subset T of a group G with the identity e is called k-thin (k∈N) if |A∩gA| ≤ k, |A∩Ag| ≤ k for every g∈G, g≠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 sys...