Metafields and Description of Metabelian Groups without the Involutions

The term quasifield is introduced for the description of metabelian groups but it also bears an independent meaning. It is proved that any finally generated metabelian group contains a generating set compared to which any element has a uniquely represented record. The elements of a group are multiplied under the formula that is defined by a characteristic numerical set. In addition, the characteristic numerical set defines the group uniquely up to isomorphisms.