关于π-正则类函数空间的基的研究

A Research on the Basis of the π-Regular Class Function Space

定义了π-可分群的主不可分解Bπ'-特征标,推广了群的主不可分解特征标的概念,得到了特征标π-理论的一些重要性质。文中的结果推广了一些著名的定理,例如,将Isaacs证明的主不可分解特征标为p-正则类函数空间的一组基的结论推广到主不可分解Bπ'-特征标为G的π-正则类函数空间的一组基,等。

The de and the concept properties on ch finition of the Bπ-principal indecomposable characters is given in the π-separable groups of the principal indecomposable characters is generalized. Furthermore, some important aractersl of π-theory are obtained. Some well know the results are generalizations of some well-known results. For instance, the theory that the principal indecomposable characters are the basis of p-regular class functions space, proved by Isaacs, is generalized in π-regular class functions space.