Research Projects

The classical group theory, developed in the 1960s, has expanded into larger groups and rings. This study focuses on unitary groups, which are isometry groups of generalized quadratic forms. The focus is on odd unitary groups over form rings, introduced by V. Petrov in 2005. These groups are generalizations of conventional classical groups and have elementary transformations called Eichler transformations. The structure theory of odd unitary groups is studied, with comparisons made between the DSER elementary orthogonal group and Petrov's odd unitary group. The Steinberg group associated with these groups is also studied. The definition of Petrov's odd unitary group is also generalized.