Criterions of supersolubility of some finite factorizable groups
Let \(A\), \(B\) be subgroups of a group \(G\) and \(\emptyset \ne X \subseteq G\). A subgroup \(A\) is said to be \(X\)-permutable with \(B\) if for some \(x\in X\) we have \(AB^x=B^xA\) [1]. We obtain some new criterions for supersolubility of a finite group \(G=AB\), where \(A\) and \(B\) are su...
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| Date: | 2018 |
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Lugansk National Taras Shevchenko University
2018
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admjournalluguniveduua-article-9272018-03-21T06:47:49Z Criterions of supersolubility of some finite factorizable groups Legchekova, Helena V. finite group, supersoluble group, permutable subgroups, product of subgroups 20D20 Let \(A\), \(B\) be subgroups of a group \(G\) and \(\emptyset \ne X \subseteq G\). A subgroup \(A\) is said to be \(X\)-permutable with \(B\) if for some \(x\in X\) we have \(AB^x=B^xA\) [1]. We obtain some new criterions for supersolubility of a finite group \(G=AB\), where \(A\) and \(B\) are supersoluble groups. In particular, we prove that a finite group \(G=AB\) is supersoluble provided \(A\), \(B\) are supersolube subgroups of \(G\) such that every primary cyclic subgroup of \(A\) \(X\)-permutes with every Sylow subgroup of \(B\) and if in return every primary cyclic subgroup of \(B\) \(X\)-permutes with every Sylow subgroup of \(A\) where \(X=F(G)\) is the Fitting subgroup of \(G\). Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/927 Algebra and Discrete Mathematics; Vol 4, No 3 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/927/456 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-03-21T06:47:49Z |
| collection |
OJS |
| language |
English |
| topic |
finite group supersoluble group permutable subgroups product of subgroups 20D20 |
| spellingShingle |
finite group supersoluble group permutable subgroups product of subgroups 20D20 Legchekova, Helena V. Criterions of supersolubility of some finite factorizable groups |
| topic_facet |
finite group supersoluble group permutable subgroups product of subgroups 20D20 |
| format |
Article |
| author |
Legchekova, Helena V. |
| author_facet |
Legchekova, Helena V. |
| author_sort |
Legchekova, Helena V. |
| title |
Criterions of supersolubility of some finite factorizable groups |
| title_short |
Criterions of supersolubility of some finite factorizable groups |
| title_full |
Criterions of supersolubility of some finite factorizable groups |
| title_fullStr |
Criterions of supersolubility of some finite factorizable groups |
| title_full_unstemmed |
Criterions of supersolubility of some finite factorizable groups |
| title_sort |
criterions of supersolubility of some finite factorizable groups |
| description |
Let \(A\), \(B\) be subgroups of a group \(G\) and \(\emptyset \ne X \subseteq G\). A subgroup \(A\) is said to be \(X\)-permutable with \(B\) if for some \(x\in X\) we have \(AB^x=B^xA\) [1]. We obtain some new criterions for supersolubility of a finite group \(G=AB\), where \(A\) and \(B\) are supersoluble groups. In particular, we prove that a finite group \(G=AB\) is supersoluble provided \(A\), \(B\) are supersolube subgroups of \(G\) such that every primary cyclic subgroup of \(A\) \(X\)-permutes with every Sylow subgroup of \(B\) and if in return every primary cyclic subgroup of \(B\) \(X\)-permutes with every Sylow subgroup of \(A\) where \(X=F(G)\) is the Fitting subgroup of \(G\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/927 |
| work_keys_str_mv |
AT legchekovahelenav criterionsofsupersolubilityofsomefinitefactorizablegroups |
| first_indexed |
2025-12-02T15:37:39Z |
| last_indexed |
2025-12-02T15:37:39Z |
| _version_ |
1850411433827762176 |