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.
