Research Projects

The study of the unit group of group algebra is an important problem in the area of group ring. Under this project, we would the like to study the normal complement problem , i.e., for what group G and ring R , G has a normal complement in the unit group of the group ring RG. If it exists, then find the normal subgroup N of the unit group U(RG) such that U(RG) can be written as semi direct product of N and G which provides the structure of U(RG). The normal complement problem also connects with isomorphism problem. For some integral group ring and some modular group algebra, mainly for p-groups, the affirmative answer of normal complement problem gives affirmative answer of isomorphism problem. Our aim is to explore normal complement problem for modular group algebras FG for finite non p-group G over a finite field F. Further, we are planning to make connection with isomorphism problem. Group algebras have been used in the area of coding theory. There is a development of linear codes by using the units of group algebra. In this direction, we would like to develop codes by using units of group algebras for these class of group algebra.

0