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Another single law for groups

Published online by Cambridge University Press:  17 April 2009

B.H. Neumann
B.H. Neumann
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, PO Box 4, Canberra, ACT 2600, Australia Division of Mathematics and Statistics, Commonwealth Scientific and Industrial Research Organization, PO Box 1965, Canberra City, ACT 2601, Australia.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1981 , pp. 81 - 102
Copyright
Copyright © Australian Mathematical Society 1981

References

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