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The paper is a continuation of the authors’ works in 2007. We consider the MD5-foliations associated to connected and simply connected MD5-groups such that their Lie algebras have 4-dimensional commutative derived ideals. In this study, we give a topological classification of all considered MD5-foliations. A description of these foliations by certain fibrations or suitable actions of ℝ2 and the Connes’...