Algebraic entropies, Hopficity and co-Hopficity of direct sums of Abelian Groups
Brendan Goldsmith, Ketao Gong (2015)
Topological Algebra and its Applications
Similarity:
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.