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Finite non-Abelian simple groups which contain a non-trivial semipermutable subgroup. (English) Zbl 1077.20024
Let $$G$$ be a finite group. A subgroup $$H$$ of $$G$$ is called semipermutable if $$H$$ permutes with every subgroup $$K$$ of $$G$$ with $$(|H|,|K|)=1$$, and it is called $$s$$-semipermutable if $$H$$ permutes with every Sylow $$p$$-subgroup of $$G$$ with $$p\nmid|H|$$.
In the paper under review the authors classify all the finite non-Abelian simple groups containing a non-trivial semipermutable or $$s$$-semipermutable subgroup.

##### MSC:
 20D05 Finite simple groups and their classification 20D40 Products of subgroups of abstract finite groups 20D20 Sylow subgroups, Sylow properties, $$\pi$$-groups, $$\pi$$-structure
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##### References:
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