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. A. Malcev constructed [1, p. 221] an interesting correspondence X between the class ST, of all nonassociative rings with identity and a certain class of groups G5, nilpotent of class at most 2. Malcev proved [1, Theorem 1, p. 226] by means of this correspondence that the theories of 9Z and G5 are equivalent. This theorem is generalized here by showing that all of nonassociative ring theory is equivalent to the theory of a larger class of groups (. We prove specifically

An equivalence between nonassociative ring theory and the theory of a special class of groups