Mathematical Sciences: Topics in Finite Group Theory

本研究涉及有限群论，特别是不动点问题和Hall-Higman理论的研究。主要研究有限单群中最长子群链的长度和有限模的置换结构问题。在此基础上，进一步研究了具有多正规子群的有限群的特征理论，研究了特征分解的性质。此外，还将讨论有限群理论领域中的其他问题，包括有限群子群的偏序集上的莫比乌斯函数问题和伽罗瓦理论问题。

This research is concerned with finite group theory,particularly the study of fixed point problems and Hall-Higman theory. The principal investigator will study problems concerning the length of the longest chain of subgroups in finite simple groups and the permutation structure of finite modules. Further, the character theory of finite groups with many normal subgroups will be examined, studying properties of character factorization. In addition, other problems in the area of finite groups theory will be considered, including problems involving the Mobius function on the poset of subgroups of a finite group and problems of Galois theory.