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On lattices of varieties of metabelian groups

Published online by Cambridge University Press:  09 April 2009

M. S. Brooks
M. S. Brooks
Affiliation:
Australian National UniversityCanberra, ACT, 2600
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This paper presents an example to show that the lattice of subvarieties of 3, 9 Λ11 is non-distributive. The example is used further to show that a certain ‘canonic” description for non-nilpotent subvarieties of pp2, p prime, is generally not unique.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 2 , May 1971 , pp. 161 - 166
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Bryce, R. A., ‘Metabelian groups and varieties’, submitted to Philos. Trans. Roy. Soc. London, Ser. A.Google Scholar
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[3]Kovács, L. G. and Newman, M. F., ‘On non-Cross varieties of groups’, to appear in J. Austral. Math. Soc.Google Scholar
[4]Neumann, Hanna, Varieties of groups, (Springer-Verlag, Berlin, 1967).CrossRefGoogle Scholar