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Necessary and suﬃcient conditions to ensure that the direct sum of two Abelian groups with zero entropy is again of zero entropy are still unknown; interestingly the same problem is also unresolved for direct sums of Hopﬁan and co-Hopﬁan groups. We obtain suﬃcient conditions in some situations by placing restrictions on the homomorphisms between the groups. There are clear similarities between the various cases but there is not a simple duality involved.
Goldsmith, B. & Kong, G. (2019). Algebraic entropies, Hopficity and co-Hopficity of direct sums of Abelian Groups. Topological Algebra and its Applications, 3(1). DOI 10.1515/taa-2015-0007