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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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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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/1126 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543374976221184 |
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| author | Kniahina, Viktoryia Nikolaevna Monakhov, Victor Stepanovich |
| author_facet | Kniahina, Viktoryia Nikolaevna Monakhov, Victor Stepanovich |
| author_sort | Kniahina, Viktoryia Nikolaevna |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-10-20T08:02:25Z |
| 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. |
| first_indexed | 2025-12-02T15:41:54Z |
| format | Article |
| id | admjournalluguniveduua-article-1126 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:41:54Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| 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 |
| title | 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_short | On finite groups with Hall normally embedded Schmidt subgroups |
| title_sort | on finite groups with hall normally embedded schmidt subgroups |
| topic | finite group Hall subgroup normal subgroup derived subgroup nilpotent subgroup 20E28 20E32 20E34 |
| topic_facet | finite group Hall subgroup normal subgroup derived subgroup nilpotent subgroup 20E28 20E32 20E34 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1126 |
| work_keys_str_mv | AT kniahinaviktoryianikolaevna onfinitegroupswithhallnormallyembeddedschmidtsubgroups AT monakhovvictorstepanovich onfinitegroupswithhallnormallyembeddedschmidtsubgroups |