On finite groups with Hall normally embedded Schmidt subgroups
A subgroup \(H\) of a finite group \(G\) is said to be Hall normally embedded in \(G\) if there is a normal subgroup \(N\) of \(G\) such that \(H\) is a Hall subgroup of \(N\). A Schmidt group is a non-nilpotent finite group whose all proper subgroups are nilpotent. In this paper, we prove that if e...
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1126 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-11262018-10-20T08:02:25Z On finite groups with Hall normally embedded Schmidt subgroups Kniahina, Viktoryia Nikolaevna Monakhov, Victor Stepanovich finite group, Hall subgroup, normal subgroup, derived subgroup, nilpotent subgroup 20E28, 20E32, 20E34 A subgroup \(H\) of a finite group \(G\) is said to be Hall normally embedded in \(G\) if there is a normal subgroup \(N\) of \(G\) such that \(H\) is a Hall subgroup of \(N\). A Schmidt group is a non-nilpotent finite group whose all proper subgroups are nilpotent. In this paper, we prove that if each Schmidt subgroup of a finite group \(G\) is Hall normally embedded in \(G\), then the derived subgroup of \(G\) is nilpotent. Lugansk National Taras Shevchenko University 2018-10-20 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1126 Algebra and Discrete Mathematics; Vol 26, No 1 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1126/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1126/353 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-10-20T08:02:25Z |
| collection |
OJS |
| language |
English |
| topic |
finite group Hall subgroup normal subgroup derived subgroup nilpotent subgroup 20E28 20E32 20E34 |
| spellingShingle |
finite group Hall subgroup normal subgroup derived subgroup nilpotent subgroup 20E28 20E32 20E34 Kniahina, Viktoryia Nikolaevna Monakhov, Victor Stepanovich On finite groups with Hall normally embedded Schmidt subgroups |
| topic_facet |
finite group Hall subgroup normal subgroup derived subgroup nilpotent subgroup 20E28 20E32 20E34 |
| format |
Article |
| author |
Kniahina, Viktoryia Nikolaevna Monakhov, Victor Stepanovich |
| author_facet |
Kniahina, Viktoryia Nikolaevna Monakhov, Victor Stepanovich |
| author_sort |
Kniahina, Viktoryia Nikolaevna |
| title |
On finite groups with Hall normally embedded Schmidt subgroups |
| title_short |
On finite groups with Hall normally embedded Schmidt subgroups |
| title_full |
On finite groups with Hall normally embedded Schmidt subgroups |
| title_fullStr |
On finite groups with Hall normally embedded Schmidt subgroups |
| title_full_unstemmed |
On finite groups with Hall normally embedded Schmidt subgroups |
| title_sort |
on finite groups with hall normally embedded schmidt subgroups |
| description |
A subgroup \(H\) of a finite group \(G\) is said to be Hall normally embedded in \(G\) if there is a normal subgroup \(N\) of \(G\) such that \(H\) is a Hall subgroup of \(N\). A Schmidt group is a non-nilpotent finite group whose all proper subgroups are nilpotent. In this paper, we prove that if each Schmidt subgroup of a finite group \(G\) is Hall normally embedded in \(G\), then the derived subgroup of \(G\) is nilpotent. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1126 |
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AT kniahinaviktoryianikolaevna onfinitegroupswithhallnormallyembeddedschmidtsubgroups AT monakhovvictorstepanovich onfinitegroupswithhallnormallyembeddedschmidtsubgroups |
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2025-07-17T10:33:18Z |
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2025-07-17T10:33:18Z |
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1837889905072537600 |