## ABSTRACT

Let G be a finite group. Denote its integral group ring by ZG and let V (ZG) be the subgroup consisting of units with augmentation 1. H. Zassenhaus stated with respect to torsion subgroups of units of V (ZG)

three conjectures [28]. ZC-1 Let u be a unit of finite order of V (ZG). Then u is conjugate within QG to an element of G.1 ZC-2 Let H be a subgroup of V (ZG) with the same order as G. Then H is conjugate within QG to G. ZC-3 Let H be a finite subgroup of V (ZG). Then H is conjugate within QG to a subgroup of G.