@article{Trofimuk_Gritsuk_2020, title={The derived $p$-length of a $p$-solvable group with bounded indices of Fitting $p$-subgroups in its normal closures}, volume={72}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/629}, DOI={10.37863/umzh.v72i3.629}, abstractNote={<p>UDC 512.542</p> <p>Let $G$ be a $p$-soluble group. Then $G$ has a subnormal series whose factors are $p^{\prime}$-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 $G.$<span class="Apple-converted-space"> </span>A subgroup<span class="Apple-converted-space"> </span>$H$ of a group $G$ is called Fitting if $H\leq F (G) .$<span class="Apple-converted-space"> </span>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.</p>}, number={3}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Trofimuk, A. A. and Gritsuk , D. V.}, year={2020}, month={Mar.}, pages={366-370} }