Using the Luthar–Passi method, we investigate the possible orders and partial augmentations of torsion units of the normalized unit group of integral group rings of Conway simple groups Co1, Co2 and Co3. Let U(ZG) be the unit group of the integral group ring ZG of a finite group G, and V (ZG) be its normalized unit group

We investigate the Zassenhaus Conjecture for the integral group ring of the simple group PSL(3, 4).

we characterize the rational subsets of a finite group and discuss the relations to integral cayley graphs.

IfG is a finite group whose integral group ring Z[G] has the multiplicative Jordan decomposition property, then it is known that all Wedderburn components of the rational group ring Q[G] have degree at most 3. While degree 3 components can occur, we prove here that if they do, then certain central units in Z[G] cannot exist. With this, we are able to greatly simplify the argument that character...