TY - JOUR
AU - A. A. Trofimuk
AU - D. V. Gritsuk
PY - 2020/03/28
Y2 - 2023/03/24
TI - The derived $p$-length of a $p$-solvable group with bounded indices of Fitting $p$-subgroups in its normal closures
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 72
IS - 3
SE - Research articles
DO - 10.37863/umzh.v72i3.629
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/629
AB - UDC 512.542Let $G$ 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.
ER -