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In this paper, we study possible zero divisors and units in $\\mathbb{F}[G]$ whose supports have size $3$. For any field $\\mathbb{F}$ and all torsion-free groups $G$, we prove that if $\\alpha \\beta=0$ for some non-zero $\\alpha, \\beta \\in \\mathbb{F}[G]$ such that $|supp(\\alpha)|=3$, then $|supp(\\beta)|\\geq 10$. 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