On weakly \(s\)-semipermutable subgroups of finite groups. II. (Q2861358)

All groups considered in this paper are finite. A subgroup \(H\) of a group \(G\) is said to be \(s\)-semipermutable in \(G\) if \(HG_p=G_pH\) for any \(p\)-Sylow subgroup \(G_p\) of \(G\) such that \((p,|H|)=1\). A subgroup \(H\) of a group \(G\) is said to be weakly \(s\)-semipermutable in \(G\) if there exists a subnormal subgroup \(T\) of \(G\) and an \(s\)-semipermutable subgroup \(H_{ssG}\) contained in \(H\) such that \(G=HT\) and \(H\cap T\leq H_{ssG}\).NEWLINENEWLINE Using the weak \(s\)-semipermutability of some primary subgroups of a group \(G\), the author obtains the \(p\)-nilpotency of the group \(G\). Also he uses the weakly \(s\)-semipermutability to characterize when a normal subgroup of \(G\) is contained in the supersoluble hypercenter of \(G\).NEWLINENEWLINE For part I see \textit{Y. Li} et al. [J. Algebra 371, 250-261 (2012; Zbl 1269.20020)].