## On $$S$$-quasinormally embedded subgroups of finite groups.(English)Zbl 1011.20019

This paper considers the consequences of a finite group $$G$$ having special families of subgroups that are $$S$$-quasinormally embedded in $$G$$. Sample result: Theorem 3.1. Let $$G$$ be a finite group and let $$p$$ be the smallest prime dividing $$|G|$$. Then the following are equivalent: (a) $$G$$ is $$p$$-nilpotent; (b) The maximal subgroups of the Sylow $$p$$-subgroups of $$G$$ are $$S$$-quasinormally embedded in $$G$$.

### MSC:

 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, $$\pi$$-length, ranks 20D20 Sylow subgroups, Sylow properties, $$\pi$$-groups, $$\pi$$-structure 20D30 Series and lattices of subgroups 20D40 Products of subgroups of abstract finite groups
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### References:

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