On the unit groups of the integral group rings of metacyclic groups

AbstractLet G be a finite group and let V(ZG) be the group of units of augmentation one of ZG. Denote by Cn the cyclic group of order n and by Cn⋊Cm the metacyclic group which is the split extension of Cn by Cm with some conditions.The main result of this paper is the following theorem: “Suppose that m is an even integer not dividing 12, then, there exist at most a finite number of primes p such that G = Cp⋊Cm has a normal complement in V(ZG.