Itô's theorem and metabelian Leibniz algebras

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We prove that the celebrated Itô's theorem for groups remains valid at the level of Leibniz algebras: if g is a Leibniz algebra such that g = A + B, for two abelian subalgebras A and B, then g is metabelian, i.e. [[g, g], [g, g]] = 0. A structure type theorem for metabelian Leibniz/Lie algebras is proved. All metabelian Leibniz algebras having the derived algebra of dimension 1 are described, classified and their automorphisms groups are explicitly determined as subgroups of a semidirect product of groups P* (k* × Autₖ (P)) associated to any vector space P.