Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-12-04T09:32:06.295Z Has data issue: false hasContentIssue false
  • English
  • Français

Note on the extensions of Butler groups

Published online by Cambridge University Press:  17 April 2009

L. Fuchs  and
G. Viljoen
L. Fuchs
Affiliation:
Department of Mathematics, Tulane University, New Orleans LA 70118, United States of America
G. Viljoen
Affiliation:
Department of Mathematics, University of Orange Free State, Bloemfontein 9300, Republic of South Africa
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.

In terms of a new notion, called prebalancedness, those extensions of a Butler group by a Butler group which are again Butler groups are characterised. It is shown that the prebalanced extensions of torsion-free abelian groups form a divisible subgroup in the group of extensions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 1 , February 1990 , pp. 117 - 122
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Albrecht, U. and Hill, P., ‘Butler groups of infinite rank and Axiom 3’, Czechoslovak Math. J. 37 (1987), 293–309.CrossRefGoogle Scholar
[2]Arnold, D.M., Finite Rank Torsion-free Abelian Groups and Rings, Lecture Notes in Math. 931 (Springer-Verlag, Berlin, Heidelberg, New York, 1982).CrossRefGoogle Scholar
[3]Fuchs, L., Infinite Abelian Groups, Vol. 1–2 (Academic Press, New York, 1970 and 1973).Google Scholar
[4]Giovannitti, A., ‘Extensions of Butler groups’, in Abelian Group Theory, Editors Göbel, R., Lady, L. and Madz, A., Lecture Notes in Math, 1006, pp. 164–170 (Springer-Verlag, Berlin, Heidelberg, New York, 1983).CrossRefGoogle Scholar
[5]Warfield, R.B., ‘Extensions of torsion-free abelian groups of finite rank’, Arch. Math. 23 (1972), 145–150.CrossRefGoogle Scholar