Another single law for groups

It has long been known that, in terms of right division, groups can be defined by a single law. In this paper a single law defining groups in terms of multiplication and inversion is proposed. This law is in 4 variables, and it is conjectured that no fewer than 4 variables will do, and that the prop...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 1981-02, Vol.23 (1), p.81-102
Main Author: Neumann, B.H.
Format: Article
Language:English
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Summary:It has long been known that, in terms of right division, groups can be defined by a single law. In this paper a single law defining groups in terms of multiplication and inversion is proposed. This law is in 4 variables, and it is conjectured that no fewer than 4 variables will do, and that the proposed law is of minimal length as well. Some extensions of the result, and an alternative single law with the same length and number of variables, are also discussed. By contrast, groups in terms of multiplication, inversion, and a unit element can not be defined by a single law. Most of these results were stated by Tarski at the Logic Colloquium at Hannover in 1966, but apparently no proof has yet been published.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972700006912