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It is shown that a torsion unit $u$ in $\\mathbb{Z}G$ mapping to the identity under the natural homomorphism $\\mathbb{Z}G \\rightarrow \\mathbb{Z}G/N$ is conjugate in the unit group of $\\mathbb{Z}_pG$ to an element in $N$. Here $\\mathbb{Z}_p$ denotes the $p$-adic integers. 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