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The influence of s-c-permutably embedded subgroups on the structure of finite groups. (English) Zbl 1228.20014
Summary: A subgroup $$H$$ of a group $$G$$ is said to be s-c-permutably embedded in $$G$$ if every Sylow subgroup of $$H$$ is a Sylow subgroup of some s-conditionally permutable subgroup of $$G$$. In this paper, some new characterizations for a finite group to be $$p$$-supersoluble or $$p$$-nilpotent are obtained under the assumption that some of its maximal subgroups or 2-maximal subgroups of Sylow subgroups are s-c-permutably embedded. A series of known results are generalized.
##### 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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