On locally soluble \(\mathrm A \mathrm F \mathrm N\)-groups

• Date: 2018
• Main Author: Dashkova, Olga Yu.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: locally soluble group; noetherian module; group ring; 20F19
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/710
• Journal Title: Algebra and Discrete Mathematics

Let \(A\) be an \({\mathbf{R}G}\)-module, where \(\bf R\) is a commutative ring, \(G\) is a locally soluble group, \(C_{G}(A)=1\), and each proper subgroup \(H\) of \(G\) for which \(A/C_{A}(H)\) is not a noetherian \(\bf R\)-module, is finitely generated. We describe the structure of a locally solu...