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The influence of $$c$$-normality of subgroups on the structure of finite groups. (English) Zbl 0967.20011
A subgroup $$H$$ of a finite group $$G$$ is $$c$$-normal if there is a normal subgroup $$G>N$$ such that $$HN=G$$ and $$H\cap N$$ lies in the core of $$H$$. The authors investigate the influence of $$c$$-normality on the structure of $$G$$, obtaining, for example, the following result on supersolvability. If $$N$$ is a normal subgroup of $$G$$ such that (1) $$G/N$$ is supersolvable and (2) $$P_1$$ is $$c$$-normal in $$G$$ for every Sylow subgroup $$P$$ of $$N$$ and every maximal subgroup $$P_1$$ of $$P$$, then $$G$$ is supersolvable.

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
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