Abstract
The complete direct sum modulo the direct sum of copies of ℤ fails to be algebraically compact as soon as the indexing set is uncountable. On the other hand, a sufficent condition is given to ensure algebraic compactness of certain smaller homomorphic images.
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Gerstner, O. Algebraische Kompaktheit bei Faktorgruppen von Gruppen ganzzahliger Abbildungen. Manuscripta Math 11, 103–109 (1974). https://doi.org/10.1007/BF01184951
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DOI: https://doi.org/10.1007/BF01184951