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Imbedded subgroups of abelian groups

Part of: Abelian groups

Published online by Cambridge University Press:  09 April 2009

W. P. Berlinghoff ,
J. D. Moore  and
J. D. Reid
W. P. Berlinghoff
Affiliation:
Colby College Waterville, Maine 04901, U.S.A.
J. D. Moore
Affiliation:
Arizona State University Tempe, Arizona 85287, U.S.A.
J. D. Reid
Affiliation:
Wesleyan University, Middletown, Connecticut 06457, U.S.A.
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Abstract

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A 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.

MSC classification

Secondary: 20K10: Torsion groups, primary groups and generalized primary groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 2 , April 1990 , pp. 281 - 298
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Fuchs, L., Infinite Abelian Groups, vol. I, Academic Press, New York, 1970.Google Scholar
[2]Fuchs, L., Infinite Abelian Groups, vol. II, Academic Press, New York, 1970.Google Scholar
[3]Head, T., ‘Remarks on a problem in primary abelian groups,’ Bull. Soc. Math. France 91 (1963), 109–112.Google Scholar
[4]Hill, P. and Megibben, C., ‘Quasi-closed primary groups,’ Acta Math. Acad. Sci. Hungar. 16 (1965), 271–274.CrossRefGoogle Scholar
[5]Megibben, C., ‘Kernels of purity in abelian groups,’ Publ. Math. Debrecen 11 (1964), 160–164.CrossRefGoogle Scholar
[6]Moore, J. D., ‘On quasi-complete abelian p-groups,’ Rocky Mountain J. Math. 5 (1975), 601–609.CrossRefGoogle Scholar
[7]Moore, J. D. and Bowman, H., ‘A note on the large subgroup topology for abelian groups,’ Comment. Math. Univ. St. Paul 22:2 (1973), 7–17.Google Scholar
[8]Moore, J. D. and Bowman, H., ‘A method for obtaining proper classes of short exact sequences of abelian groups,’ Publ. Math. Debrecen 24 (1977), 59–63.Google Scholar