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Let $Aut(\\mathcal{X})$ be the group of all automorphisms of $\\mathcal{X}$ which fix $\\mathbb{K}$ element-wise. For any solvable subgroup $G$ of $Aut(\\mathcal{X})$ we prove that $|G|\\leq 34 (\\mathcal{g}(\\mathcal{X})+1)^{3/2}$. There are known curves attaining this bound up to the constant $34$. 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