Nonunits of group algebras over the fours group

Abstract

The conjecture on units of group algebras of a torsion-free supersoluble group is saying that every unit is trivial, i.e. a product of a nonzero element of the field and an element of the group. This conjecture is still open and even in the slightly simple case of the fours group σ = (x,y|(x2)y = x-2, (y2)x = y-2), it is not yet known. The main result of this paper is to show that a wide range of elements of group algebra of σ are nonunit. © 2019 World Scientific Publishing Company.