This project is concerned with the subgroup structure of finite and algebraic groups of Lie type. The principal investigator will consider general reductive overgroups and the minimal connected overgroup of arbitrary unipotent elements. She will also examine certain triples of quasisimple groups of Lie type in an effort to classify the maximal subgroups of the finite classical groups. Finally she will work on extending a homomorphism of finite groups of Lie type to a morphism of suitable algebraic groups. A group is an algebraic object with a single operation defined on it. Groups occur naturally in many different areas of mathematics, as well as, physics and chemistry. During the last decade, many researchers have worked on determining the subgroup structure of finite simple groups of Lie type. The approach used in this project is to view the question on finite groups in the context of algebraic groups.
