有限群零化元比例与群结构

本项目深化、扩展了已有的工作，拟研究有限群的零化元比例对其结构的影响。主要研究内容为：.1. 当有限群的零化元比例小于7次交错群的零化元比例时，刻画该有限群的结构；.2. 研究非 p-可解群零化元比例的下确界x，并考察当有限群零化元比例小于x时，该群Sylow p-子群的性质。.本项目的研究一定程度上阐明了有限群零化元比例与有限群结构之间的关系，这为我们最终理解有限群的零化元奠定了基础。

In this project, we develop existing work and plan to study the influence of the proportion of vanishing elements of finite groups on their structure. And we mainly focus on the following topics: .1. Given that the proportion of vanishing elements of a finite group is less than the proportion of vanishing elements of the alternating group of degree 7, we intend to study the group's structure..2. We intend to study the infimum x of the proportion of vanishing elements of non-p-solvable groups. Given that the proportion of vanishing elements of a finite group is less than x, we also intend to study the properties of Sylow p-subgroups of the group..To some extent, our study reveals some connection between the proportion of vanishing elements of finite groups and the groups' structure, which lays the foundation for us to understand the vanishing elements of finite groups.