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 \(...
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| Дата: | 2020 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2020
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1317 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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. |
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