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The influence of $$s$$-semipermutable subgroups on the structure of finite groups. (Chinese. English summary) Zbl 1119.20026
Summary: A subgroup $$H$$ of a group $$G$$ is said to be semipermutable if it is permutable with every subgroup $$K$$ of $$G$$ with $$(|H|,|K|)=1$$, and $$s$$-semipermutable if it is permutable with every Sylow $$p$$-subgroup of $$G$$ with $$(p,|H|)=1$$. In this paper, we extend and improve some of Asaad’s and P.-C. Wang’s results by examining the influence of $$s$$-semipermutability on the structure of groups.

##### 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