Hostname: page-component-6d856f89d9-sp8b6 Total loading time: 0 Render date: 2024-07-16T07:49:03.171Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
[2]Cohen, D. E., ‘On the laws of a metabelian variety’, J. Algebra 5 (1967), 267–273.CrossRefGoogle Scholar
[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