The derived $p$-length of a $p$-solvable group with bounded indices of Fitting $p$-subgroups in its normal closures

• Datum: 2020
• Hauptverfasser: Trofimuk, A. A., Gritsuk , D. V., Трофимчук, А. А., Грицук, Д. В., Трофімчук, О.О.
• Format: Artikel
• Sprache: Russisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2020
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/629
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 512.542 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 $G.$  A subgroup  $H$ of a group $G$ is called Fitting if $H\leq F (G) .$  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.