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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.

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