The influence of weakly \(s\)-permutable subgroups on the \(p\)-nilpotency of finite groups. (Chinese. English summary) Zbl 1240.20030
Summary: Let \(G\) be a finite group. A subgroup \(H\) of \(G\) is called weakly \(s\)-permutable in \(G\) if \(G\) has a subnormal subgroup \(T\) such that \(G=HT\) and \(H\cap T\leq H_{sG}\), where \(H_{sG}\) is the largest \(s\)-quasinormal subgroup of \(G\) contained in \(H\). The influence of weakly \(s\)-permutability of maximal subgroups of Sylow subgroups of a finite group on its \(p\)-nilpotency is investigated. A generalization of Schur-Zassenhaus theorem is given in the paper.
MSC:
| 20D40 | Products of subgroups of abstract finite groups |
| 20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
