Linear groups saturated by subgroups of finite central dimension

• Date: 2020
• Main Authors: Semko, N. N., Skaskiv, L. V., Yarovaya, O. A.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2020
• Subjects: linear group; infinite group; infinite dimensional linear group; dense family of subgroups; locally soluble group; finite central dimension; Primary 20E15; 20F16; Secondary 20E25; 20E34; 20F22; 20F50
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1317
• Journal Title: Algebra and Discrete Mathematics

Let \(F\) be a field, \(A\) be a vector space over \(F\) and \(G\) be a subgroup of \(\mathrm{GL}(F,A)\). We say that \(G\) has a dense family of subgroups, having finite central dimension, if for every pair of subgroups \(H\), \(K\) of \(G\) such that \(H\leqslant K\) and \(H\) is not maximal in \(...