Linear groups saturated by subgroups of finite central dimension
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 \(...
Saved in:
| Date: | 2020 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2020
|
| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1317 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | 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 \(K\) there exists a subgroup \(L\) of finite central dimension such that \(H\leqslant L\leqslant K\). In this paper we study some locally soluble linear groups with a dense family of subgroups, having finite central dimension. |
|---|