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

Khan, M. A.

doi:10.1090/S0002-9939-1981-0619998-X

When are proper subgroups of LCA groups contained in maximal ones?
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Proc. Amer. Math. Soc. 83 (1981), 131-137 Request permission

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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