A Study On The Characteristic Of B _{π '} - Characteristic

Based on the results of previous studies, further research on the monomial of B_π’-character is carried on in this paper. In the first chapter, some basic concepts and basic results are collected about p-theories of characters.In the second chapter, some properties of direct product of finite groups about π-theories of characters are given. In the third chapter, the direct product of B_π’-single character are introduced and some results about M_π-group are extend to the M_π-group（see Theorem 3.8 and Theorem 3.9）.In the fourth chaper, the wreath product of B_π’-single character are discussed（see Theorem 4.5）.