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For a finite group $G$, let $\tilde{\mathbb{Z}}$ be the semilocalization of$\mathbb{Z}$ at the prime divisors of $|G|$. If $G$ is a Frobenius group withFrobenius kernel $K$, it is shown that each torsion unit in the group ring$\tilde{\mathbb{Z}} G$ which maps to the identity under the natural ringhomomorphism $\tilde{\mathbb{Z}} G \rightarrow \tilde{\mathbb{Z}} G/K$ isconjugate to an element of $G$ by a unit in $\tilde{\mathbb{Z}} G$.

On torsion units in integral group rings of Frobenius groups