On pure subgroups of $\textrm {LCA}$ groups
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- by D. L. Armacost PDF
- Proc. Amer. Math. Soc. 45 (1974), 414-418 Request permission
Abstract:
In this note we determine the structure of those locally compact abelian (LCA) groups in which no nontrivial closed subgroup is pure and the structure of those LCA groups in which every closed subgroup is pure.References
- D. L. Armacost and W. L. Armacost, On $p$-thetic groups, Pacific J. Math. 41 (1972), 295–301. MR 330343, DOI 10.2140/pjm.1972.41.295
- Jean Braconnier, Sur les groupes topologiques localement compacts, J. Math. Pures Appl. (9) 27 (1948), 1–85 (French). MR 25473
- László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
- S. Hartman and A. Hulanicki, Les sous-groupes purs et leurs duals, Fund. Math. 45 (1957), 71–77 (French). MR 92102, DOI 10.4064/fm-45-1-71-77
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496, DOI 10.1007/978-1-4419-8638-2
- Irving Kaplansky, Infinite abelian groups, University of Michigan Press, Ann Arbor, 1954. MR 0065561
- Martin Moskowitz, Homological algebra in locally compact abelian groups, Trans. Amer. Math. Soc. 127 (1967), 361–404. MR 215016, DOI 10.1090/S0002-9947-1967-0215016-3 L. Robertson, Transfinite torsion, $p$-constituents, and splitting in locally compact abelian groups (unpublished).
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 45 (1974), 414-418
- MSC: Primary 22B05
- DOI: https://doi.org/10.1090/S0002-9939-1974-0346087-0
- MathSciNet review: 0346087