On derived \(\pi\)-length of a finite \(\pi\)-solvable group with supersolvable \(\pi\)-Hall subgroup
It is proved that if \(\pi\)-Hall subgroup is a supersolvable group then the derived \(\pi\)-length of a \(\pi\)-solvable group \(G\) is at most \(1+ \max_{r\in \pi}l_r^a(G),\) where \(l_r^a(G)\) is the derived \(r\)-length of a \(\pi\)-solvable group \(G.\)
Збережено в:
| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1160 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543374488633344 |
|---|---|
| author | Monakhov, V. S. Gritsuk, D. V. |
| author_facet | Monakhov, V. S. Gritsuk, D. V. |
| author_sort | Monakhov, V. S. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-05-16T05:04:06Z |
| description | It is proved that if \(\pi\)-Hall subgroup is a supersolvable group then the derived \(\pi\)-length of a \(\pi\)-solvable group \(G\) is at most \(1+ \max_{r\in \pi}l_r^a(G),\) where \(l_r^a(G)\) is the derived \(r\)-length of a \(\pi\)-solvable group \(G.\) |
| first_indexed | 2025-12-02T15:41:58Z |
| format | Article |
| id | admjournalluguniveduua-article-1160 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:41:58Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-11602018-05-16T05:04:06Z On derived \(\pi\)-length of a finite \(\pi\)-solvable group with supersolvable \(\pi\)-Hall subgroup Monakhov, V. S. Gritsuk, D. V. finite group, \(\pi\)-soluble group, supersolvable group, \(\pi\)-Hall subgroup, derived \(\pi\)-length 20D10, 20D20, 20F16 It is proved that if \(\pi\)-Hall subgroup is a supersolvable group then the derived \(\pi\)-length of a \(\pi\)-solvable group \(G\) is at most \(1+ \max_{r\in \pi}l_r^a(G),\) where \(l_r^a(G)\) is the derived \(r\)-length of a \(\pi\)-solvable group \(G.\) Lugansk National Taras Shevchenko University 2018-05-16 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1160 Algebra and Discrete Mathematics; Vol 16, No 2 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1160/652 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | finite group \(\pi\)-soluble group supersolvable group \(\pi\)-Hall subgroup derived \(\pi\)-length 20D10 20D20 20F16 Monakhov, V. S. Gritsuk, D. V. On derived \(\pi\)-length of a finite \(\pi\)-solvable group with supersolvable \(\pi\)-Hall subgroup |
| title | On derived \(\pi\)-length of a finite \(\pi\)-solvable group with supersolvable \(\pi\)-Hall subgroup |
| title_full | On derived \(\pi\)-length of a finite \(\pi\)-solvable group with supersolvable \(\pi\)-Hall subgroup |
| title_fullStr | On derived \(\pi\)-length of a finite \(\pi\)-solvable group with supersolvable \(\pi\)-Hall subgroup |
| title_full_unstemmed | On derived \(\pi\)-length of a finite \(\pi\)-solvable group with supersolvable \(\pi\)-Hall subgroup |
| title_short | On derived \(\pi\)-length of a finite \(\pi\)-solvable group with supersolvable \(\pi\)-Hall subgroup |
| title_sort | on derived \(\pi\)-length of a finite \(\pi\)-solvable group with supersolvable \(\pi\)-hall subgroup |
| topic | finite group \(\pi\)-soluble group supersolvable group \(\pi\)-Hall subgroup derived \(\pi\)-length 20D10 20D20 20F16 |
| topic_facet | finite group \(\pi\)-soluble group supersolvable group \(\pi\)-Hall subgroup derived \(\pi\)-length 20D10 20D20 20F16 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1160 |
| work_keys_str_mv | AT monakhovvs onderivedpilengthofafinitepisolvablegroupwithsupersolvablepihallsubgroup AT gritsukdv onderivedpilengthofafinitepisolvablegroupwithsupersolvablepihallsubgroup |