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Annihilator equivalence of torsion-free abelian groups

Part of: Abelian groups

Published online by Cambridge University Press:  09 April 2009

P. Schultz ,
C. Vinsonhaler  and
W. J. Wickless
P. Schultz
Affiliation:
The University of Western AustraliaNedlands, Western Australia, 6009, Australia
C. Vinsonhaler
Affiliation:
University of Connecticut, Storrs, Connecticut, 06268, U.S.A.
W. J. Wickless
Affiliation:
University of Connecticut, Storrs, Connecticut, 06268, U.S.A.
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Abstract

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We define an equivalence relation on the class of torsion-free abelian groups under which two groups are equivalent ifevery pure subgroup of one has a non-zero image in the other, and each has a non-zero image in every torsion-free factor of the other.

We study the closure properties of the equivalence classes, and the structural properties of the class of all equivalence classes. Finally we identify a class of groups which satisfy Krull-Schmidt and Jordan-Hölder properties with respect to the equivalence.

MSC classification

Secondary: 20K15: Torsion-free groups, finite rank
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 52 , Issue 1 , February 1992 , pp. 119 - 129
Copyright
Copyright © Australian Mathematical Society 1992

References

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[4]Schultz, P., Annihilator Classes of Torsion-free Abelian Groups, in Topics in Algebra, Lecture Notes in Mathematics 697, Springer-Verlag, Berlin, Heidelberg and New York, 1978.CrossRefGoogle Scholar
[5]Wickless, W. J., An equivalence relation for torsion-free groups of finite rank, preprint.Google Scholar