The study of groups available as products of two Abelian subgroups was, if not initiated, so speeded up with the well known and remarkable result of Ito: Any such a product is soluble of length at most 2. Many new results have been added during the last decades and a need to write a comprehensive treatment on the afore- mentioned subject appeared. The present text collects many more or less known results on products, the exposition is unified and, in many cases, the theorems are supplied with the new proofs. Besides, new results on products of cyclic groups are added. Moreover, an introduction to the theory of commutative radical rings and a generalizations to connected transversal are included.

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