子群的完全置换性对σ-幂零根的影响OACSTPCD

Similar to the influence on nilpotent residual of the totally permutability of subgroups,naturally,we can study their influence on σ-nilpotent residual when nilpotent groups are generalized to σ-nilpotent groups.The intersection of all normal subgroups N of G such that G/N is σ-nilpotent is called σ-nilpotent residual of G,and is denoted as GNσ.Let G=AB,where A and B are totally permutable subgroups of G,this paper gives some new conclusions that B normalises ANσ and centralises ANσ by using the concepts and theories of σ-nilpotent subgroups and σ-supersoluble subgroups,and by applying some properties and methods of complete Hall σ-set and finite group theory.