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\begin{document}$$K[X_n]$$\end{document} be the commutative polynomial algebra in the variables Xn={x1,…,xn}\documentclass[12pt]{minimal}
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\begin{document}$$X_n=\{x_1,\ldots ,x_n\}$$\end{document} over a field K of characteristic zero. A theorem from undergraduate course of algebra states that the algebra K[Xn]Sn\documentclass[12pt]{minimal}
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\begin{document}$$K[X_n]^{S_n}$$\end{document} of symmetric polynomials is generated by the elementary symmetric polynomials which are algebraically independent over K. In the present paper, we study a noncommutative and nonassociative analogue of the algebra K[Xn]Sn\documentclass[12pt]{minimal}
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\begin{document}$$K[X_n]^{S_n}$$\end{document} replacing K[Xn]\documentclass[12pt]{minimal}
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\begin{document}$$K[X_n]$$\end{document} with the free metabelian Lie algebra Fn\documentclass[12pt]{minimal}
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\begin{document}$$F_n$$\end{document} of rank n≥2\documentclass[12pt]{minimal}
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\begin{document}$$n\ge 2$$\end{document} over K. It is known that the algebra FnSn\documentclass[12pt]{minimal}
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\begin{document}$$F_n^{S_n}$$\end{document} is not finitely generated, but its ideal (Fn′)Sn\documentclass[12pt]{minimal}
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\begin{document}$$(F_n')^{S_n}$$\end{document} consisting of the elements of FnSn\documentclass[12pt]{minimal}
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\begin{document}$$F_n^{S_n}$$\end{document} in the commutator ideal Fn′\documentclass[12pt]{minimal}
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\begin{document}$$F_n'$$\end{document} of Fn\documentclass[12pt]{minimal}
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\begin{document}$$F_n$$\end{document} is a finitely generated K[Xn]Sn\documentclass[12pt]{minimal}
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\begin{document}$$K[X_n]^{S_n}$$\end{document}-module. In our main result, we describe the generators of the K[Xn]Sn\documentclass[12pt]{minimal}
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\begin{document}$$K[X_n]^{S_n}$$\end{document}-module (Fn′)Sn\documentclass[12pt]{minimal}
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\begin{document}$$(F_n')^{S_n}$$\end{document} which gives the complete description of the algebra FnSn\documentclass[12pt]{minimal}
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\begin{document}$$F_n^{S_n}$$\end{document}.
