Yet another single law for groups
type: Item
instance of: scholarly article
title: Yet another single law for groups
zbMATH Open document ID: 0581.20004
published in: Illinois Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 20A05
zbMATH DE Number: 3929248
zbMATH Keywords: axioms
zbMATH Keywords: binary operation
zbMATH Keywords: right division
zbMATH Keywords: binary multiplication
zbMATH Keywords: unary inversion
zbMATH Keywords: multiplication of inverses
zbMATH Keywords: nullary operation
author: B. H. Neumann
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3929248