Research On B_π - Signature Properties

On the basis of predecessors’ work in the literature, we are further discussed the π- theoretic of characters. In the first chapter, some basic concepts and basic results which this paper need are given, In the second chapter, We proposed the use of the substitution of Brauer lemma in the B_π-characters. In the third chapter, We defined the principle indecomposable B_π’-characters,and discussed the relationship between the principle indecomposable B_π’-characters and B_π’-characters,and proved that the result that the principle indecomposable B_π’-characters are the base of p-regular class function space, In the fourth chapter, We discussed the nature of the degerees of B_π’-characters(for details see theorem 4.1 and 4.2).