Groups, in which almost all subgroups are near to normal
A subgroup \(H\) of a group \(G\) is said to be nearly normal, if \(H\) has a finite index in its normal closure. These subgroups have been introduced by B.H. Neumann. In a present paper is studied the groups whose non polycyclic by finite subgroups are nearly normal. It is not hard to show that und...
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| Date: | 2018 |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/993 |
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admjournalluguniveduua-article-9932018-05-15T05:12:44Z Groups, in which almost all subgroups are near to normal Semko, M. M. Kuchmenko, S. M. A subgroup \(H\) of a group \(G\) is said to be nearly normal, if \(H\) has a finite index in its normal closure. These subgroups have been introduced by B.H. Neumann. In a present paper is studied the groups whose non polycyclic by finite subgroups are nearly normal. It is not hard to show that under some natural restrictions these groups either have a finite derived subgroup or belong to the class \(S_{1}F\) (the class of soluble by finite minimax groups). More precisely, this paper is dedicated of the study of \(S_{1}F\) groups whose non polycyclic by finite subgroups are nearly normal. Lugansk National Taras Shevchenko University 2018-05-15 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/993 Algebra and Discrete Mathematics; Vol 3, No 2 (2004) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/993/522 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2018-05-15T05:12:44Z |
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OJS |
| language |
English |
| topic |
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| spellingShingle |
Semko, M. M. Kuchmenko, S. M. Groups, in which almost all subgroups are near to normal |
| topic_facet |
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| format |
Article |
| author |
Semko, M. M. Kuchmenko, S. M. |
| author_facet |
Semko, M. M. Kuchmenko, S. M. |
| author_sort |
Semko, M. M. |
| title |
Groups, in which almost all subgroups are near to normal |
| title_short |
Groups, in which almost all subgroups are near to normal |
| title_full |
Groups, in which almost all subgroups are near to normal |
| title_fullStr |
Groups, in which almost all subgroups are near to normal |
| title_full_unstemmed |
Groups, in which almost all subgroups are near to normal |
| title_sort |
groups, in which almost all subgroups are near to normal |
| description |
A subgroup \(H\) of a group \(G\) is said to be nearly normal, if \(H\) has a finite index in its normal closure. These subgroups have been introduced by B.H. Neumann. In a present paper is studied the groups whose non polycyclic by finite subgroups are nearly normal. It is not hard to show that under some natural restrictions these groups either have a finite derived subgroup or belong to the class \(S_{1}F\) (the class of soluble by finite minimax groups). More precisely, this paper is dedicated of the study of \(S_{1}F\) groups whose non polycyclic by finite subgroups are nearly normal. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/993 |
| work_keys_str_mv |
AT semkomm groupsinwhichalmostallsubgroupsareneartonormal AT kuchmenkosm groupsinwhichalmostallsubgroupsareneartonormal |
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2025-12-02T15:43:48Z |
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2025-12-02T15:43:48Z |
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1850411820897009664 |