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From this definition it follows that a group is a 2-group in the above sense. The axioms used by Allen in [1] and by Ušan in [14] concern some classes of n-groups derived from 2-groups. Several authors have investigated n-groups (for a bibliography see Kuroš's book [7]), for example Timm in [12] treated commutative n-groups. It is worthwhile to note that, under the assumption 1, it suffices only to postulate the existence of a solution of (2) at the places k= 1 and k= n or at one place