On the crossing of maximal subgroups of finite groups

Abstract

UDC 517.542
We establish the structure of normghal subgroups in $\theta$-Frattini extensions, where $\theta$ is a subgroup functor. For a local Fitting structure $\frak F$ containing all nilpotent groups, it is shown that, in a solvable group, the crossing of $\frak F$-abnormal maximal $\theta$-subgroups not containing $\frak F$-radicals and not belonging to $\frak F$ coincides with the crossing of $\frak F$-abnormal maximal $\theta$-subgroups and belongs to the structure of $\frak F.$