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.
School of Mathematics and Statistics, Hubei Engineering University, No. 272, Jiaotong Road, Xiaogan City, Hubei Province, 432000, P.R.China
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