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 \(G.\)
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1160 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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 \(G.\) |
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