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For a hypersurface germ $(V,0)$ with an isolated singularity, we characterize the generic elements in the space of holomorphic vector fields with isolated singularity in terms of the GSV-index. Letting $\\tau(V,0)$ denote the Tjurina-Greuel number, we prove that the minimal possible index is bounded below by $1+(-1)^{\\dim(V)}\\tau(V,0)$. 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