LAUSR

We establish the structure of normal subgroups in θ -Frattini extensions, where θ is a subgroup functor. For a local Fitting structure F $$ \mathfrak{F} $$ containing all nilpotent groups, it is shown that, in a soluble group, the crossing of F $$ \mathfrak{F} $$ -abnormal maximal θ -subgroups not containing F $$ \mathfrak{F} $$ -radicals and not belonging to F $$ \mathfrak{F} $$ coincides with the crossing of F $$ \mathfrak{F} $$ -abnormal maximal θ -subgroups and belongs to the structure of F $$ \mathfrak{F} $$ .