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 $$ \mathfrak{F} $$ .

中文翻译：

---

关于有限群的极大子群的交叉

我们在 θ -Frattini 扩展中建立正规子群的结构，其中 θ 是子群函子。对于包含所有幂零群的局部拟合结构 F $$ \mathfrak{F} $$，表明在可溶群中，F $$ \mathfrak{F} $$ -异常极大值 θ -子群的交叉不包含 F $$ \mathfrak{F} $$ -radicals 并且不属于 F $$ \mathfrak{F} $$ 与 F $$ \mathfrak{F} $$ -abnormal maxal θ -subgroups 和属于到 F $$ \mathfrak{F} $$ 的结构。