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Denote by $\\mathfrak{g}^{e}$ the centralizer of $e$ in $\\mathfrak{g}$ and by ${\\rm S}(\\mathfrak{g}^{e})^{\\mathfrak{g}^{e}}$ the algebra of symmetric invariants of $\\mathfrak{g}^{e}$. We say that $e$ is good if the nullvariety of some $\\ell$ homogenous elements of ${\\rm S}(\\mathfrak{g}^{e})^{\\mathfrak{g}^{e}}$ in $(\\mathfrak{g}^{e})^{*}$ has codimension $\\ell$. 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Denote by $\\mathfrak{g}^{e}$ the centralizer of $e$ in $\\mathfrak{g}$ and by ${\\rm S}(\\mathfrak{g}^{e})^{\\mathfrak{g}^{e}}$ the algebra of symmetric invariants of $\\mathfrak{g}^{e}$. We say that $e$ is good if the nullvariety of some $\\ell$ homogenous elements of ${\\rm S}(\\mathfrak{g}^{e})^{\\mathfrak{g}^{e}}$ in $(\\mathfrak{g}^{e})^{*}$ has codimension $\\ell$. 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