On the non–periodic groups, whose subgroups of infinite special rank are transitively normal

• Date: 2020
• Main Authors: Kurdachenko, L. A., Subbotin, I. Ya., Velychko, T. V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2020
• Subjects: finite special rank; soluble group; periodic group; locally nilpotent radical; locally nilpotent residual; transitively normal subgroups; Primary 20E15; 20F16; Secondary 20E25; 20E34; 20F22; 20F50
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1357
• Journal Title: Algebra and Discrete Mathematics

This paper devoted to the non-periodic locally generalized radical groups, whose subgroups of infinite special rank are transitively normal. We proved that if such a~group \(G\) includes an ascendant locally nilpotent subgroup of infinite special rank, then \(G\) is abelian.