Structure of Unitary Unit Group of Finite Group Algebras

On behalf of the Department of Mathematics and Statistics of theCollege of Arts and Sciences, you are cordially invited to a seminar to beconducted by Dr. Zahid Raza from University of Sharjah, UAE.

Abstract

The theory of group rings is a meetingpoint of various algebraic theories, taking into account its central role inthe development of the theory of group representations. Since integral grouprings are of special interest for researchers and the topic involves the use ofalgebraic numbers, algebraic number theory also has an important role in thedevelopment of the subject. It is worthwhile to mention that group rings areimportant in other branches of mathematics, such as homological algebra,algebraic topology and algebraic K-theory. The existence of free subgroups inthe unit groups of group rings of finite groups has been established. There isanother important subgroup of the unite group of a group algebra which iscalled unitary unite group. Many researchers have been trying to give exactstructural representations of these special units during last fifteen years.But till now they only able to give for finite groups of very small order. Wegive the first general characterization of this subgroup for a special group oforder 2^n along with some finite groups of orders 16.

Forfurther details, kindly contact Dr. Ayman Badawi ([email protected]).