A generalization of groups with many almost normal subgroups

• Date: 2018
• Main Author: Russo, Francesco G.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Dietzmann classes; anti-\(\mathfrak{X}C\)-groups; groups with \(\mathfrak{X}\)-classes of conjugate subgroups; Chernikov groups; 20C07; 20D10; 20F24
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/623
• Journal Title: Algebra and Discrete Mathematics

A subgroup \(H\) of a group \(G\) is called almost normal in \(G\) if it has finitely many conjugates in \(G\). A classic result of B. H. Neumann informs us that \(|G:\mathbf{Z}(G)|\) is finite if and only if each \(H\) is almost normal in \(G\). Starting from this result, we investigate the structu...