On a Subclass of 5-Dimensional Solvable Lie Algebras Which Have 3-Dimensional Commutative Derived Ideal

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The paper presents a subclass of the class of MD5-algebras and MD5-groups, i.e., five dimensional solvable Lie algebras and Lie groups such that their orbits in the co-adjoint representation (K-orbit) are orbit of zero or maximal dimension. The main results of the paper is the classification up to an isomorphism of all MD5-algebras G with the derived ideal G¹:= [G, G] is a 3-dimensional commutative Lie algebra.