有限群不可约特征标维数对群结构及表代数结构的影响研究

在本项目中，我们将研究如下两大类问题：一、特征标维数性质与群结构的关系，将继续研究特征标维数幂图及群阶对单群唯一确定性，具体对Lie型中G_2(q),F_4(q),E_6(q),E_7(q),E_8(q),^2B_2(q),^3D_4(q),^2G_2(q),^2F_4(q),^2E_6(q)等进行研，并进一步研究其它非单群的特征标维数幂图和阶对群结构的影响。 二、特征标代数蕴含的表代数及正规整表代数的分类。将寻找有限群不可约特征标代数中蕴含的了由一个维数为2的忠实元素生成且线性基元个数|L_1(B)|>1正规整表代数，并研究分类L_1(B)是循环群、以及L_1(B)不循环且|L_1(B)|为特殊值的正规整表代数。

In this project, we shall study two topics. The first is to study relation between the degrees of irreducible characters of a finite group and its structure. We shall continue to study if the order of a simple group and its character degree-power graph can uniquely determine the simple group, in detail, we plan to study if it is correct for G_2(q), F_4(q), E_6(q), E_7(q), E_8(q), ^2B_2(q), ^3D_4(q), ^2G_2(q), ^2F_4(q) and ^2E_6(q), and study the same topic for non-simple groups. The second is to the implicit table algebra from character algebra of a finite group and classification of normalized integral table algebra. We shall try to find the implicit table algebra normalized integral table algebras from character algebra of a finite group and generated by a faithful element of degree 2 and having non-identical linear base elements, i.e., |L_1(B)|>1. Further to classify normalized integral table algebras with L_1(B) cyclic, or L_1(B) non-cyclic, but |L_1(B)| is of special numbers.