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On the laws of some varieties of groups

Published online by Cambridge University Press:  09 April 2009

M. R. Vaughan-Lee
M. R. Vaughan-Lee
Affiliation:
Vanderbilt UniversityNashville Tennessee
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D. E. Cohen has shown in [1] that a variety consisting of metabelian groups has a finite basis for its laws. In this paper I make use of Cohen's result to prove the following theorem.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 3 , August 1970 , pp. 353 - 356
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Cohen, D. E., ‘On the Laws Of A Metabelian Variety’; Journal of Algebra, 5 (1967), 267–273.Google Scholar
[2]Neumann, Hanna, Varieties of Groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 37).CrossRefGoogle Scholar
[3]Hall, P., ‘Finiteness Conditions for Soluble Groups’, Proc. London Math. Soc., (3), 4 (1954), 419–436.Google Scholar