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The intrinsic algebraic entropy ent(ɸ) of an endomorphism ɸ of an Abelian group G can be computed using fully inert subgroups of ɸ-invariant sections of G, instead of the whole family of ɸ-inert subgroups. For a class of groups containing the groups of finite rank, aswell as those groupswhich are trajectories of finitely generated subgroups, it is proved that only fully inert subgroups of the group...
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...
If $$G$$ G is a Hopfian abelian group then it is, in general, difficult to determine if direct sums of copies of $$G$$ G will remain Hopfian. We exhibit large classes of Hopfian groups such that every finite direct sum of copies of the group is Hopfian. We also show that for any integer $$n > 1$$ n > 1 there is a torsion-free Hopfian group $$G$$ G having...
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