Imbedded subgroups of abelian groups
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Published:1990-04
Issue:2
Volume:48
Page:281-298
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ISSN:0263-6115
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Container-title:Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
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language:en
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Short-container-title:J Aust Math Soc A
Author:
Berlinghoff W. P.,Moore J. D.,Reid J. D.
Abstract
AbstractA subgroup H of an abelian p–group G is pure in G if the inclusion map of H into G is an isometry with respect to the (pseudo-) metrics on H and G associated with their p–adic topologies. In this paper, those subgroups (called here imbedded subgroups) of abelian groups for which the inclusion is a homeomorphism with respect to the p–adic topologies are studied, the aim being to compare the concepts of imbeddedness and purity. Perhaps the main results indicate that imbedded subgroups are considerably more abundant than pure subgroups. Groups for which this is not the case are characterized.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics,Statistics and Probability
Reference8 articles.
1. A method for obtaining proper classes of short exact sequences of abelian groups;Moore;Publ. Math. Debrecen,1977
2. A note on the large subgroup topology for abelian groups;Moore;Comment. Math. Univ. St. Paul,1973
3. On quasi-complete abelian $p$-groups
4. Kernels of purity in abelian groups;Megibben;Publ. Math. Debrecen,1964
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