Yet another single law for groups
It has long been known that groups can be axiomatized by a single law in terms of a binary operation, right division [\textit{G. Higman} and \textit{B. H. Neumann}, Publ. Math., Debrecen 2, 215-221 (1953; Zbl 0050.25303)]. Much later it was shown that a single law also suffices to define groups in terms of the binary multiplication and the unary inversion [\textit{B. H. Neumann}, Bull. Aust. Math. Soc. 23, 81-102 (1981; reviewed above)]. In the present paper, answering a question asked by R. Padmanabhan, it is shown that groups can also be axiomatized by a single law in terms of a binary operation, namely multiplication of inverses, and the nullary operation that produces the unit element; or also in terms of the same binary operation and the unary inversion. The method is similar to that in the earlier papers. Some unsolved problems are stated.
scientific article; zbMATH DE number 3929248
scientific article