Groups with many pronormal and transitively normal subgroups

• Date: 2018
• Main Authors: Kurdachenko, L. A., Semko (Jr.), N. N., Subbotin, I. Ya.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: soluble group; radical group; locally nilpotent group,transitively normal subgroup; non finitely generated subgroup; 20E15; 20F19
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/713
• Journal Title: Algebra and Discrete Mathematics

A subgroup \(H\) of a group \(G\) is said to be transitively  normal in \(G\), if \(H\) is normal in every subgroup \(K\geqslant H\) such that \(H\) is subnormal in \(K\). We described some infinite groups, whose non–finitely generated subgroups are transitively normal.