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Two examples in varieties of monoids

Published online by Cambridge University Press:  24 October 2008

John R. Isbell
John R. Isbell
Affiliation:
State University of New York at Buffalo
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Extract

This note exhibits an infinite independent set of laws for monoids (viz. (xpyp)2 = (ypxp)2, p prime) and a variety of groups defined by one law (which is x2y2 = y2x2) such that the smallest containing variety of monoids is not finitely definable.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 2 , September 1970 , pp. 265 - 266
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Evans, Trevor. The number of semigroup varieties. Quart. J. Math. Oxford Ser. 2, 19 (1968), 335–336.CrossRefGoogle Scholar
(2)Fajtlowicz, S.Birkhoff's theorem in the category of non-indexed algebras. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 17 (1969), 273–275.Google Scholar
(3)Lewin, Jacques and Lewin, Tekla. Semigroup laws in varieties of solvable groups. Proc. Cambridge Philos. Soc. 65 (1969), 1–9.CrossRefGoogle Scholar