Let ZG be the integral group ring of a finite group G. Denote by UZG the group of units and by U1ZG those of augmentation one. A well-known conjecture of Zassenhaus states:

(ZC1): If u ∈ U1ZG is a torsion unit then u is rationally conjugate to a group element. That is, there exist elements g ∈ G, β ∈ U lQG such that, β−1uβ = g.