Let G be a finite group.Fix a prime divisor p of |G| and a Sylow p-subgroup P of G,let d be the smallest generator number of P and Md(P) denote a family of maximal subgroups P1,P2,...,Pd of P satisfying di=1 Pi = Φ(P),the Frattini subgroup of P.In this paper,we shall investigate the influence of s-conditional permutability of the members of some fixed Md(P) on the structure of finite groups.Some new results are obtained and some known results are generalized.
In this paper the influence of s-quasinormally embedded and c-supplemented subgroups on the p-nilpotency of finite groups is investigate and some recent results are generalized.
