The derived $p$-length of a $p$-solvable group with bounded indices of Fitting $p$-subgroups in its normal closures - Trofimuk, A. A.; Gritsuk , D. V. (Ukrains’kyi Matematychnyi Zhurnal, 2020)
UDC 512.542Let $G$ be a $p$-soluble group. Then $G$ has a subnormal series whose factors are $p^{′}$-groups or abelian $p$-groups. The smallest number of abelian $p$-factors of all such subnormal series of~$G$ is called the derived $p$-length of $G.$ A subgroup $H$ of a group $G$ is called Fitting if $H≤ F (G) .$ A functional dependence of the estimate of the derived $p$-length of a $p$-soluble group on the value of the indexes of Fitting $p$-subgroups in its normal closures is established.