On relations between generalized norms in locally finite groups

• Date: 2025
• Main Authors: Lukashova, Tetiana, Drushlyak, Marina
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2025
• Subjects: norm of a group; generalized norms; norm of Abelian non-cyclic subgroups of a group; norm of decomposable subgroups of a group; non- Dedekindness; locally finite group
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2347
• Journal Title: Algebra and Discrete Mathematics

In the paper the relations between such generalized norms as the norm of Abelian non-cyclic subgroups and the norm of decomposable subgroups in the class of infinite locally finite groups are studied. The local nilpotency and non-Dedekindness of the norm of Abelian non-cyclic subgroups are considere...