On derived \(\pi\)-length of a finite \(\pi\)-solvable group with supersolvable \(\pi\)-Hall subgroup

• Date: 2018
• Main Authors: Monakhov, V. S., Gritsuk, D. V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: finite group; \(\pi\)-soluble group; supersolvable group; \(\pi\)-Hall subgroup; derived \(\pi\)-length; 20D10; 20D20; 20F16
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1160
• Journal Title: Algebra and Discrete Mathematics

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 \(G.\)