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\(c^*\)-normal and \(s\)-semipermutable subgroups in finite groups. (English) Zbl 1336.20024

Summary: A subgroup \(H\) of a group \(G\) is called \(c^*\)-normal in \(G\) if there exists a normal subgroup \(N\) of \(G\) such that \(G=HN\) and \(H\cap N\) is \(S\)-quasinormally embedded in \(G\). A subgroup \(K\) of \(G\) is said to be \(s\)-semipermutable if it is permutable with every Sylow \(p\)-subgroup of \(G\) with \((p,|K|)=1\). In this article, we investigate the influence of \(c^*\)-normality and \(s\)-semipermutability of subgroups on the structure of finite groups and generalize some known results.

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
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