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Militaru","submitted_at":"2014-01-19T14:52:18Z","abstract_excerpt":"We prove that the celebrated It\\^{o}'s theorem for groups remains valid at the level of Leibniz algebras: if $\\mathfrak{g}$ is a Leibniz algebra such that $\\mathfrak{g} = A + B$, for two abelian subalgebras $A$ and $B$, then $\\mathfrak{g}$ is metabelian, i.e. $[ \\, [\\mathfrak{g}, \\, \\mathfrak{g}], \\, [ \\mathfrak{g}, \\, \\mathfrak{g} ] \\, ] = 0$. A structure type theorem for metabelian Leibniz/Lie algebras is proved. 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