The Selection Of Dade Basis Of A Finite P-Group

In this paper,we discuss the specific structure of the set of Dade bases of p-group in a special representation,that is to say,if the p-group is represented by a triangular representation,we determine the necessary and sufficient condition for when ?1,…,?n? V*is a Dade basis.The structure of this paper is as follows:In the introduction,we review some basic research of invariant theory.In the first chapter,we introduce some related knowledge,such as what is the parameter system,what is the Dade basis and the definition of Chen's orbit class,and then we give some important conclusions about the Dade basis.In the second chapter,we start with a few simple examples,and discuss when the dual basis will be a Dade basis of p order cyclic group in CharFq = p = q.In chapter three,we discuss the necessary and sufficient conditions for when the dual basis will be a Dade basis of p-group.Finally,there is an example illustrates when p ? q,the conclusion cannot be generalized.