The Influence of Some Weakly c-normal Subgroups on the Structure of Finite Groups

Let G be a finite group,a subgroup H of a group G is called weakly c-nornal if there exists a subnormal subgroup K of G such that G=HK and H∩K≤HG=∩g∈GHg,where HG is the largest normal subgroup of G contained in H.In this paper,in terms of weakly c-normal subgroups,some sufficient conditions for a finite group to be supersolvable or nilpotent are obtained.And some known results are generalized.