Abstract
An investigation of the structure of locally compact abelian groups whose lattices of closed subgroups satisfy Dedekind's axiom. This condition is closely related to the finite-rank condition. In contrast to the discrete case, Dedekind groups form a relatively small subclass of the class of all locally compact abelian groups. A description is given of abelian groups such that the product of any two closed subgroups is closed.
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Translated from Matematicheskie Zametki, Vol. 8, No. 4, pp. 509–520, October, 1970.
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Mukhin, Y.N. Topological abelian groups with a Dedekind lattice of closed subgroups. Mathematical Notes of the Academy of Sciences of the USSR 8, 755–760 (1970). https://doi.org/10.1007/BF01104378
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DOI: https://doi.org/10.1007/BF01104378