On S-Quasinormally Embedded Subgroups of Prime Power Order in Finite Groups

摘要

Let C be a p-solvable finite group, where p is an odd prime divisor of |G|, and P be a Sylow p-subgroup of G with the smallest generator number d. Consider the set .M_d(P) ={P_1,...P_d}, where P_1...P_d are the maximal subgroups of P such that d P_i =(P). It isshown that if every member of M_d(P) is S-quasinormally embedded in G, then G is p-supersolvable. As its applications, some further results are obtained.