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Some infinitely based varieties of groups

Published online by Cambridge University Press:  09 April 2009

Roger M. Bryant
Roger M. Bryant
Affiliation:
Australian National UniversityCanberra, Act, 2600
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Problem 11 of Hanna Neumann's book [3] asks whether the product variety Β4Β2 has a finite basis for its laws. (For any positive integer k, Βk denotes the variety of all groups of exponent diving k.) I think that Β4Β2 was being suggested as a plausible canditate for a variety without the finite basis property; of course, at a time when no such example was known. It is the primary object of this note to verify the fact that Β4Β2 is not finitely based. Β4Β2 provides, therefore, probably the simplest example known at present of a variety which is not finitely based.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 1 , August 1973 , pp. 29 - 32
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Brooks, M. S., Kov´cs, 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
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