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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
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Abstract

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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
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