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Generalization of the Schur-Zassenhaus theorem. (English) Zbl 0935.20013
The main results of this paper are as follows: (1) If a Hall $$\pi$$-subgroup $$H$$ of a finite group $$G$$ is $$S$$-seminormal in $$G$$, then $$H$$ has a complement in $$G$$ and all such complements are conjugate in $$G$$. (2) If the Sylow $$p$$-subgroups of a finite group $$G$$ are $$S$$-seminormal in $$G$$, then $$G$$ is $$p$$-solvable.

##### MSC:
 20D20 Sylow subgroups, Sylow properties, $$\pi$$-groups, $$\pi$$-structure 20D40 Products of subgroups of abstract finite groups 20D35 Subnormal subgroups of abstract finite groups 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, $$\pi$$-length, ranks