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On product varieties of groups

Published online by Cambridge University Press:  17 April 2009

M.R. Vaughan-Lee
M.R. Vaughan-Lee
Affiliation:
University of Queensland, St Lucia, Queensland, and Christ Church, Oxford.
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Abstract

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An example is given of a finitely based variety of groups such that is not finitely based.

Let be the variety of groups determined by the laws (1) [[x1, x2], [x3, x4, [x5, x6]], (2) [[x1, x2, x3], [x4, x5]] [[x1x2], [x4, x5, x3]]−1, [[x1, x2, x3], [x1, x2]]. Then is not finitely based.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 2 , October 1971 , pp. 239 - 240
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Brooks, M.S., Kovács, L.G. and Newman, M.F., “A finite basis theorem for product varieties of groups”, Bull. Austral. Math. Soc. 2 (1970), 39–44.CrossRefGoogle Scholar
[2]Newman, M.F., “Just non-finitely-based varieties of groups”, Bull. Austral. Math. Soc. 4 (1971), 343–348.CrossRefGoogle Scholar
[3]Vaughan-Lee, M.R., “Uncountably many varieties of groups”, Bull. London Math. Soc. 2 (1970), 280–286.CrossRefGoogle Scholar