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

Abstract

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 \(G.\)