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The well-known Bachmuth-Mochizuki-Roman'kov Theorem \cite{BM,Romankov85}states that every automorphism of the free metabelian group of rank $\geq 4$ istame. In 1992 Yu. Bahturin and S. Nabiyev \cite{BN} claimed that everynontrivial inner automorphism of the free metabelian Lie algebra $M_n$ of anyrank $n\geq 2$ over a field of characteristic zero is wild. More examples ofwild automorphisms of $M_n$ of rank $n\geq 4$ were given in 2008 by Z. \"Ozcurtand N. Ekici \cite{OE}. The main goal of this note is to show that botharticles contain uncorrectable errors and to draw the attention of specialiststo the fact that the question of tame and wild automorphisms for freemetabelian Lie algebras $M_n$ of rank $n\geq 4$ is still widely open.

Erroneous proofs of the wildness of some automorphisms of free metabelian Lie algebras