The P～＊-Nilpotency And θ-Pairs For Subgroups On Finite Groups

It is important to study the structures of finite groups by combining some subgroups with some properties in the researches on finite groups. In this paper, we discuss the following:(1) The relations between the θ-pairs of maximal subgroups and c-normality , weak c- normality , s-normality , the normal index of maximal subgroups;(2) Some results on solvablity of finite groups that are obtained by using the s-normality of subgroups;(3) The θ-pairs of general proper subgroups of finite groups as the generalization of the θ-pairs of maximal subgroups that is used to describe c-normal subgroups , weak c- normal subgroups and s-normal subgroups, by which some new results on finite groups are obtained;(4) Some new results on p-quasinilpotent groups and p*-nilpotent groups.