The Influence Of C-normality And θ-pairs Of Subgroups On The Structure Of Finite Groups

In this paper, we study the relationship between the structure of finite groups and the c-normality and θ— pairs of some subgroups . The main results are the following:(1) We obtain some sufficient conditions on solvablity of finite groups by the c— normality of Sylow subgroups and 2— maximal subgroups.(2) We obtain some results on solvability and nilpotency of finite groups by the 9— pairs of 2—maximal subgroups.(3) We obtain some results on solvablity and supersolvablity of finite groups by 9— pairs of Sylow subgroups and Sylow normalizers.