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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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/993 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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. |
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