Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-15T01:10:07.735Z Has data issue: false hasContentIssue false
  • English
  • Français

ANOTHER LAW FOR 3-METABELIAN GROUPS

Published online by Cambridge University Press:  30 March 2012

CHRISTINE BUSSMAN and
DAVID A. JACKSON
CHRISTINE BUSSMAN
Affiliation:
Department of Mathematics, Saint Louis University, St. Louis, MO 63103, USA e-mail: olearyck@geek-den.net
DAVID A. JACKSON
Affiliation:
Department of Mathematics, Saint Louis University, St. Louis, MO 63103, USA e-mail: jacksoda@slu.edu
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.

We show that [z, y]−1[z, x]−1[y, x]−1[z, y][z, x][y, x] = 1 is another defining law for the variety of 3-metabelian groups.

Keywords

20E10

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 3 , September 2012, pp. 627 - 628
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

REFERENCES

1.Bachmuth, S. and Lewin, J., The Jacobi identity in groups, Math. Z. 83 (1964), 170–176.Google Scholar
2.Jackson, D. A., Gaglione, A. M. and Spellman, D., Basic commutators as relators, J. Group Theory 5 (2002), 351–363.Google Scholar
3.Jackson, D. A., Gaglione, A. M. and Spellman, D., Weight five basic commutators as relators, in Computational group theory and the theory of groups, II, Contemporary Mathematics 511 (American Mathematical Society, Providence, RI, 2010), 39–81.Google Scholar
4.Macdonald, I. D., On certain varieties of groups, Math. Z. 76 (1961), 270–282.Google Scholar
5.Macdonald, I. D., On certain varieties of groups II, Math. Z. 78 (1962), 175–188.Google Scholar
6.Macdonald, I. D., Another law for the 3-metabelian groups, J. Austral. Math. Soc. 4 (1964), 452–453. Corrigendum, J. Austral. Math. Soc. 6 (1966), 512.Google Scholar
7.Neumann, B. H., On a conjecture of Hanna Neumann, Proc. Glasgow Math. Assoc. 3 (1956), 13–17.CrossRefGoogle Scholar
8.Neumann, H., Varieties of groups (Springer-Verlag, New York, 1967).CrossRefGoogle Scholar