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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0619998-X
PII: S 0002-9939(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