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When are proper subgroups of LCA groups contained in maximal ones?


Author: M. A. Khan
Journal: Proc. Amer. Math. Soc. 83 (1981), 131-137
MSC: Primary 22B05; Secondary 20K27
DOI: https://doi.org/10.1090/S0002-9939-1981-0619998-X
MathSciNet review: 619998
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Abstract: In this note we determine (1) the class of LCA groups for which every proper closed subgroup is contained in a maximal subgroup, (2) the class of LCA groups for which every proper dense subgroup is contained in a maximal subgroup, and (3) the class for which every proper subgroup is contained in a maximal one. We also determine when both an LCA group and its dual have these properties.


References [Enhancements On Off] (What's this?)

  • [1] D. L. Armacost and W. L. Armacost, On $ Q$-dense and densely divisible LCA groups, Proc. Amer. Math. Soc. 36 (1972), 301-305. MR 0306401 (46:5527)
  • [2] W. E. Dietrich, Jr., Dense decompositions of locally compact groups, Colloq. Math. 24 (1972), 147-151. MR 0318388 (47:6935)
  • [3] L. Fuchs, Infinite abelian groups. Vol. 1, Academic Press, New York, 1970. MR 0255673 (41:333)
  • [4] E. Hewitt and K. A. Ross, Abstract harmonic analysis. Vol. 1, Die Grundlehren der math. Wissenschaften, Band 115, Academic Press, New York; Springer-Verlag, Berlin, 1963.
  • [5] M. A. Khan, Chain conditions on subgroups of LCA groups, Pacific J. Math. 86 (1980), 517-534. MR 590565 (82b:22004)
  • [6] H. L. Peterson, Discontinuous characters and subgroups of finite index, Pacific J. Math. 44 (1973), 683-691. MR 0316627 (47:5174)
  • [7] M. Rajagopalan and H. Subrahmanian, Dense subgroups of locally compact groups, Colloq. Math. 35 (1976), 289-292. MR 0417325 (54:5381)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0619998-X
Keywords: Maximal subgroups, reduced, totally reduced, divisible, abelian groups, locally compact abelian, $ p$-adic integers, quasicyclic
Article copyright: © Copyright 1981 American Mathematical Society

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