This research is concerned with the structure of classical groups including orthogonal, symplectic and unitary groups over rings with involutions. The principal investigator will study normal and subnormal subgroups, automorphisms and isomorphisms. Waring's problem and related problems for commutative and matrix rings will also be considered. This research is in the general area of algebraic K-theory. Algebraic K-theory has become an important area of mathematics since it has led to the solution of some interesting problems in mathematics. This project is concerned with a wide variety of qualitative and quantitative problems related to subgroups of algebraic groups. The anticipated outcome of this research will be significant for the mathematical community.
