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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| Date: | 2020 |
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Lugansk National Taras Shevchenko University
2020
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admjournalluguniveduua-article-13172020-05-14T18:27:22Z Linear groups saturated by subgroups of finite central dimension Semko, N. N. Skaskiv, L. V. Yarovaya, O. A. 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 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. Lugansk National Taras Shevchenko University 2020-05-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1317 10.12958/adm1317 Algebra and Discrete Mathematics; Vol 29, No 1 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1317/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1317/488 Copyright (c) 2020 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2020-05-14T18:27:22Z |
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OJS |
| language |
English |
| topic |
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 |
| spellingShingle |
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 Semko, N. N. Skaskiv, L. V. Yarovaya, O. A. Linear groups saturated by subgroups of finite central dimension |
| topic_facet |
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 |
| format |
Article |
| author |
Semko, N. N. Skaskiv, L. V. Yarovaya, O. A. |
| author_facet |
Semko, N. N. Skaskiv, L. V. Yarovaya, O. A. |
| author_sort |
Semko, N. N. |
| title |
Linear groups saturated by subgroups of finite central dimension |
| title_short |
Linear groups saturated by subgroups of finite central dimension |
| title_full |
Linear groups saturated by subgroups of finite central dimension |
| title_fullStr |
Linear groups saturated by subgroups of finite central dimension |
| title_full_unstemmed |
Linear groups saturated by subgroups of finite central dimension |
| title_sort |
linear groups saturated by subgroups of finite central dimension |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2020 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1317 |
| work_keys_str_mv |
AT semkonn lineargroupssaturatedbysubgroupsoffinitecentraldimension AT skaskivlv lineargroupssaturatedbysubgroupsoffinitecentraldimension AT yarovayaoa lineargroupssaturatedbysubgroupsoffinitecentraldimension |
| first_indexed |
2025-12-02T15:44:07Z |
| last_indexed |
2025-12-02T15:44:07Z |
| _version_ |
1850411841196392448 |