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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.

20D05 Finite simple groups and their classification
20D40 Products of subgroups of abstract finite groups
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
Full Text: DOI
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