The Application Of Finite Group Transfer Theory In Related Formal Complements

To study the conditions for the existence of related normal complement of subgroup of finite groups has always been an important subject.In this paper,by studying the theory of finite group transfer and related normal complement,we mainly have done the folloing work: Firstly,some basic properties of transfer theory and some basic results used in this paper are summarized.Secondly,the different forms of transfer homomorphism have been studied,It has proved that these different forms of transfer homomorphism are equivalent.Finally,some sufficient conditions for a finite group to have normal complement and relative normal complement are given by using the transfer theory.