The influence of weakly c-normal and ss-quasinormal subgroups of prime power order on the structure of finite groups

摘要

Let P be a Sylow p-subgroup of the finite group G for some prime p. Let P_1,P_2,...,P_d be maximal subgroups of P such that ∩P_i=Φ (P) is the Frattini subgroup of P. Assume that the P_i′s are ss-quasinormal or weakly c-normal in G (in the sense of Li, Shen, Zhu, Wang and others). We give sufficient conditions on p and G implying that G is p-nilpotent or p-supersoluble.