Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-24T13:22:51.629Z Has data issue: false hasContentIssue false
  • English
  • Français

The laws of some metabelian varieties

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Richard Levingston
Richard Levingston
Affiliation:
Department of Mathematics, Institute of Advanced Studies, The Australian National University, P.O. Box 4, Canberra, A.C.T. 2600, Australia
Rights & Permissions [Opens in a new window]

Abstract

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.

It is shown that if m, n are relatively prime positive integers, then the variety consisting of those soluble groups of exponent mn in which any subgroup of exponent m or n is abelian has a basis of two-variable laws.

MSC classification

Secondary: 20E10: Quasivarieties and varieties of groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 4 , April 1981 , pp. 469 - 472
Copyright
Copyright © Australian Mathematical Society 1981

References

Gorenstein, D. (1968), Finite groups (Harper and Row, New York, Evanston, London).Google Scholar
Higman, G. (1959), ‘Some remarks on varieties of groups’, Quart. J. Math. Oxford Ser. 10, 165–178.CrossRefGoogle Scholar
Neumann, H. (1967), Varieties of groups (Ergebnisse der Mathematik und ihrer Grenzgebiete 37, Springer-Verlag, Berlin, Heidelberg, New York).CrossRefGoogle Scholar