This award supports research in the area of finite group theory. The principal investigator will study "fixed point" problems, including cases where the operator group is not solvable. He will look into the character theory of finite groups with many normal subgroups, using character factorization techniques among others, to reduce questions about arbitrary finite groups to questions about finite (almost) simple groups. He will also look into the theory of the finite almost simple groups, extending and refining his results on the maximum length of chains of subgroups and Schur index formulas, among others. A group is an algebraic structure with a single operation. It appears in many areas of mathematics, as well as, physics and chemistry. The fundamental building blocks of finite groups are finite simple groups. One of the major results in mathematics of the past decade is the classification of the finite simple groups, the proof of which would require 10,000 to 15,000 journal pages. This research goes beyond the classification theorem to provide further information about finite groups.
