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Just non-finitely-based varieties of groups

Published online by Cambridge University Press:  17 April 2009

M.F. Newman
M.F. Newman
Affiliation:
Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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A variety of groups is just non-finitely-based if it does not have a finite basis for its laws while all its proper subvarieties do have a finite basis. Recent work of Ol'šanskiiˇ, Vaughan-Lee and Adjan guarantees the existence of at least one just non-finitely-based variety. In this note an infinite number of just non-finitely-based varieties are shown to exist by proving that for every prime p there is a non-finitely based variety of p–groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 3 , June 1971 , pp. 343 - 348
Copyright
Copyright © Australian Mathematical Society 1971

References

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