ON s-PERMUTABLY EMBEDDED AND WEAKLY c-NORMAL SUBGROUPS OF FINITE GROUPS

Abstract

Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G with the smallest generator number d. We consider such a set Md(P) = {P1, P2, . . . , Pd} of maximal subgroups of P such that ∩di=1Pi = Φ(P). Groups with certain s-permutably embedded and weakly c-normal subgroups of prime power order are studied. We present some sufficient conditions for a group to be p-nilpotent or p-supersolvable.