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Varieties of nilpotent groups of class four (III)
Published online by Cambridge University Press: 09 April 2009
Abstract
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In this paper we complete the investigation of those varieties of nilpotent groups of class (at most) four whose free groups have no nontrivial elements of odd order. Each such variety is labelled by a vector of sixteen parameters, each parameter a nonnegative integer or ∞, subject to numerous but simple conditions. Each vector satisfying these conditions is in fact used and directly yields a defining set of laws for the variety it labels. Moreover, one can easily recognise from the parameters whether one variety is contained in another. In view of the reduction carried out in the first paper of this series (written jointly with L. G. Kovács) this completes the determination of all varieties of nilpotent groups of class four.
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- Research Article
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- Copyright
- Copyright © Australian Mathematical Society 1983
References
Fitzatrick, Patrick and Kovács, L. G., ‘Varieties of nilpotent groups of class four (I)’, J. Austral. Math. Soc., Ser. A 35 (1983), 59–73.CrossRefGoogle Scholar
Fitzpatrick, Patrick, ‘Varieties of nilpotent groups of class four (II)’, J. Austral. Math. Soc., Ser. A. 35 (1983), 74–108.Google Scholar
Jónsson, B., ‘Varieties of groups of nilpotency three’, Notices Amer. Math. Soc. 13 (1966), 488.Google Scholar
Neumann, H., Varieties of groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, 37. Springer-Verlag, Berlin, Heidelberg, New York, 1967).Google Scholar
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