Zassenhaus Conjecture for cyclic-by-abelian groups

Abstract

Zassenhaus Conjecture for torsion units states that every augmentation 1 torsion unit of the integral group ring of a finite group G is conjugate to an element of G in the units of the rational group algebra ℚ G. This conjecture has been proved for nilpotent groups, metacyclic groups and some other families of groups. It has been also proved for some special groups. We prove the conjecture for cyclic-by-abelian groups.