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Finite groups with $$sn$$-embedded or $$s$$-embedded subgroups. (English) Zbl 1286.20019
Summary: A number of authors have studied the structure of a finite group $$G$$ under the assumption that some subgroups of $$G$$ are well located in $$G$$. We generalize the notion of $$s$$-permutable and $$s$$-permutably embedded subgroups and we obtain new criteria of $$p$$-nilpotency and supersolvability of groups. We also generalize some known results.

##### MSC:
 20D40 Products of subgroups of abstract finite groups 20D20 Sylow subgroups, Sylow properties, $$\pi$$-groups, $$\pi$$-structure 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, $$\pi$$-length, ranks 20D15 Finite nilpotent groups, $$p$$-groups
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