| This paper is about any function between finite groups,which show that arbitrary function techniques affecting the structure of the group in finite group theory.In this paper,the author introduces the anti-conjugate of the function,and anti-distributor of function.And we define the group inverse action by anti-homomorphism,the concept of inverse orbit and inverse stability subgroup can be obtained by studying the situation of group inverse action.At the same time,the author gives some discriminant theorems of anti-homomorphism by anti-distributor of function.Then we get some characterizations on the structure of finite groups by anti-homomorphism.Finally,this paper applies the views of group inverse action giving a proof of Schur-Zassenhaus theorem. |
