A Fischer Class Of Finite Group

The appearance and development of the theories of group classes were closely related to the theories of finite solvable group. It developed on the foundation of the research of finite solvable group.In this paper, we construct a Fischer class which is closely connected with the theory of finite simple group. In the investigation of the property and the structure of this Fischer class, we notice that any finite group is a subgroup of one group which belongs to this Fischer class. We also consider the F-radical and F-injector of a group and the boundary of this Fischer class in this paper.