Finite groups with semi-subnormal Schmidt subgroups
A Schmidt group is a non-nilpotent group in which every proper subgroup is nilpotent. A subgroup \(A\) of a group \(G\) is semi-normal in \(G\) if there exists a subgroup \(B\) of \(G\) such that \(G=AB\) and \(AB_1\) is a proper subgroup of \(G\) for every proper subgroup \(B_1\) of \(B\). If \(A\)...
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| Дата: | 2020 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2020
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1376 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| id |
admjournalluguniveduua-article-1376 |
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admjournalluguniveduua-article-13762020-05-14T18:27:22Z Finite groups with semi-subnormal Schmidt subgroups Kniahina, V. N. Monakhov, V. S. finite soluble group, Schmidt subgroup, semi-normal subgroup, subnormal subgroup 20E28, 20E32, 20E34 A Schmidt group is a non-nilpotent group in which every proper subgroup is nilpotent. A subgroup \(A\) of a group \(G\) is semi-normal in \(G\) if there exists a subgroup \(B\) of \(G\) such that \(G=AB\) and \(AB_1\) is a proper subgroup of \(G\) for every proper subgroup \(B_1\) of \(B\). If \(A\) is either subnormal in \(G\) or is semi-normal in \(G\), then \(A\) is called a semi-subnormal subgroup of \(G\). In this paper, we establish that a group \(G\) with semi-subnormal Schmidt \(\{2,3\}\)-subgroups is \(3\)-soluble. Moreover, if all 5-closed Schmidt \(\{2,5 \}\)-subgroups are semi-subnormal in \(G\), then \(G\) is soluble. We prove that a group with semi-subnormal Schmidt subgroups is metanilpotent. Lugansk National Taras Shevchenko University 2020-05-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1376 10.12958/adm1376 Algebra and Discrete Mathematics; Vol 29, No 1 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1376/pdf Copyright (c) 2020 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2020-05-14T18:27:22Z |
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OJS |
| language |
English |
| topic |
finite soluble group Schmidt subgroup semi-normal subgroup subnormal subgroup 20E28 20E32 20E34 |
| spellingShingle |
finite soluble group Schmidt subgroup semi-normal subgroup subnormal subgroup 20E28 20E32 20E34 Kniahina, V. N. Monakhov, V. S. Finite groups with semi-subnormal Schmidt subgroups |
| topic_facet |
finite soluble group Schmidt subgroup semi-normal subgroup subnormal subgroup 20E28 20E32 20E34 |
| format |
Article |
| author |
Kniahina, V. N. Monakhov, V. S. |
| author_facet |
Kniahina, V. N. Monakhov, V. S. |
| author_sort |
Kniahina, V. N. |
| title |
Finite groups with semi-subnormal Schmidt subgroups |
| title_short |
Finite groups with semi-subnormal Schmidt subgroups |
| title_full |
Finite groups with semi-subnormal Schmidt subgroups |
| title_fullStr |
Finite groups with semi-subnormal Schmidt subgroups |
| title_full_unstemmed |
Finite groups with semi-subnormal Schmidt subgroups |
| title_sort |
finite groups with semi-subnormal schmidt subgroups |
| description |
A Schmidt group is a non-nilpotent group in which every proper subgroup is nilpotent. A subgroup \(A\) of a group \(G\) is semi-normal in \(G\) if there exists a subgroup \(B\) of \(G\) such that \(G=AB\) and \(AB_1\) is a proper subgroup of \(G\) for every proper subgroup \(B_1\) of \(B\). If \(A\) is either subnormal in \(G\) or is semi-normal in \(G\), then \(A\) is called a semi-subnormal subgroup of \(G\). In this paper, we establish that a group \(G\) with semi-subnormal Schmidt \(\{2,3\}\)-subgroups is \(3\)-soluble. Moreover, if all 5-closed Schmidt \(\{2,5 \}\)-subgroups are semi-subnormal in \(G\), then \(G\) is soluble. We prove that a group with semi-subnormal Schmidt subgroups is metanilpotent. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2020 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1376 |
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AT kniahinavn finitegroupswithsemisubnormalschmidtsubgroups AT monakhovvs finitegroupswithsemisubnormalschmidtsubgroups |
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2025-12-02T15:38:49Z |
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2025-12-02T15:38:49Z |
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