有限群的极大子群与置换特征标

The theory of finite group plays an important role in modern mathematics and other science, such as Combination design, Cryptography, Computer science and Information science. It is quite clear that some arithmetic condition of degrees of irreducible characters and certain properties of some families of subgroups of a finite group often give a lot of information about its structure. In this project, we study the structure of finite groups by means of arithmetical conditions on maximal subgroups and degrees of permutaion character in finite groups.

有限群论在现代数学和诸多科技领域有着非常广泛的应用，特别是在当今信息时代，有限群对组合设计、密码学、计算机科学、信息安全等学科的发展产生深刻的影响。众所周知，子群的性质和特征标次数的算术条件与有限群的结构有密切联系。本项目拟研究极大子群的某些特征性质以及置换特征标等某些特殊特征标的次数的算术条件与有限群结构之间的内在联系，以揭示有限群的本质，推进某些著名问题的研究。本项目对凝聚和稳定西部地区基础科学研究人才队伍有重要意义。

本项目研究了极大子群的某些特征性质以及置换特征标等某些特殊特征标的次数的算术条件与有限群结构之间的内在联系，得到了若干有意义的结果，揭示了有限群的本质。到目前为止，本项目已经完成了该项目的研究内容，发表了27篇学术论文。