On the structure of some groups having finite contranormal subgroups

• Date: 2021
• Main Authors: Kurdachenko, L. A., Semko, N. N.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2021
• Subjects: contranormal subgroups; Abelian-by-nilpotent groups; hypercenter of a group; \(G\)-eccentric subgroups; rationally irreducible subgroups; 20E99; 20F18; 20F19
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1724
• Journal Title: Algebra and Discrete Mathematics

Following J.S. Rose, a subgroup \(H\) of the group \(G\) is said to be contranormal in \(G\), if \(G=H^{G}\). In a certain sense, contranormal subgroups are antipodes to subnormal subgroups. We study the structure of Abelian-by-nilpotent groups having a finite proper contranormal \(p\)-subgroup.