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
Main Authors: Semko, N. N., Skaskiv, L. V., Yarovaya, O. A.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2020
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Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1317
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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spelling 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
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2020-05-14T18:27:22Z
collection 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
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