Groups, in which almost all subgroups are near to normal

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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Дата:2018
Автори: Semko, M. M., Kuchmenko, S. M.
Формат: Стаття
Мова:English
Опубліковано: Lugansk National Taras Shevchenko University 2018
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Онлайн доступ:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/993
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Назва журналу:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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spelling oai:ojs.admjournal.luguniv.edu.ua: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
institution Algebra and Discrete Mathematics
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datestamp_date 2018-05-15T05:12:44Z
collection OJS
language English
topic

spellingShingle

Semko, M. M.
Kuchmenko, S. M.
Groups, in which almost all subgroups are near to normal
topic_facet

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
first_indexed 2025-07-17T10:34:06Z
last_indexed 2025-07-17T10:34:06Z
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