Mathematical Sciences: Groups and Rings

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This award is concerned with work in finite group theory. The principal investigator is interested in those groups, such as solvable groups and certain related families, which have an ample supply of normal subgroups. The primary concern is with the character theory of these groups. In particular, he will investigate the interactions between certain characters of a group, characters of particular subgroups and sets of prime numbers. He will also continue to work on questions related to the theory of M-groups. 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 is aimed at using this classification in the study of arbitrary finite groups.