We establish the structure of normal subgroups in θ-Frattini extensions, where θ is a subgroup functor. For a local Fitting structure \( \mathfrak{F} \) containing all nilpotent groups, it is shown that, in a soluble group, the crossing of \( \mathfrak{F} \)-abnormal maximal θ -subgroups not containing \( \mathfrak{F} \)-radicals and not belonging to \( \mathfrak{F} \) coincides with the crossing of \( \mathfrak{F} \)-abnormal maximal θ -subgroups and belongs to the structure of \( \mathfrak{F} \).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 11, pp. 1455–1465, November, 2019.
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Borodich, R.V. On the Crossing of Maximal Subgroups of Finite Groups. Ukr Math J 71, 1664–1676 (2020). https://doi.org/10.1007/s11253-020-01740-x
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DOI: https://doi.org/10.1007/s11253-020-01740-x