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Abelian Groups in Which Every α-Pure Subgroup is β-Pure

Published online by Cambridge University Press:  20 November 2018

J. Douglas Moore  and
Edwin J. Hewett
J. Douglas Moore
Affiliation:
Arizona State University, Tempe, Arizona
Edwin J. Hewett
Affiliation:
Arizona State University, Tempe, Arizona
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The determination of the abelian groups in which every neat subgroup is pure is a relatively routine exercise (see [6]). There are numerous problems of this type; for example, the determination of the groups in which every pure subgroup is isotype or the groups in which every subgroup is isotype. These are all special cases of the general problem of determining the abelian groups in which every α-pure subgroup is β-pure for arbitrary ordinal numbers α and β. The solution of this general problem is the object of this paper.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 3 , June 1973 , pp. 560 - 566
Copyright
Copyright © Canadian Mathematical Society 1973

References

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