Mathematical Sciences: Linear, Classical, and Chevalley Groups Over Rings

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This grant supports the research of Professors Costa and Keller to study the normal subgroups of the linear, classical and Chevalley groups over rings. They want to extend the results already obtained for the special linear and spin groups to the linear groups of type B, G and F. They also intend to study the relationship between subgroups of the special linear group of dimension 2 over a local field and Hilbert symbols. This is research in the field of algebra. This area can be thought of as the study of symmetry in the abstract. As such, this area has direct applications to many areas of physics and chemistry. Moreover, within the last 30 years, many connections to problems in data transmission have been solved using techniques from group theory. There are also direct connections to the error correcting codes that are vital for modern computing such as working with CD-ROM's as well as to theoretical computer science in general.