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On $$c$$-normal maximal and minimal subgroups of Sylow $$p$$-subgroups of finite groups. (English) Zbl 1050.20010
A subgroup $$H$$ of a finite group $$G$$ is said to be $$c$$-normal in $$G$$ if there exists a subgroup $$N$$ of $$G$$ such that $$G=HN$$ and $$H\cap N$$ is contained in $$\text{Core}_G(H)$$, the largest normal subgroup of $$G$$ contained in $$H$$. For a prime $$p$$, the authors study the influence of the $$c$$-normality of the maximal subgroups of the Sylow $$p$$-subgroups of a group and the $$c$$-normality of some minimal subgroups on the structure of a group. They find some criteria for a finite group $$G$$ to be $$p$$-nilpotent, $$p$$-supersoluble, or to belong to a saturated formation.

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