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Subgroups of the Baer-Specker Group with Few Endomorphisms but Large Dual

The Baer-Specker group is the product of countably many copies of the additive group Z of integers. Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer-Specker group with the following properties. Every endomorphism of G differs from a scalar multiplication by an endomorphism of finite rank. Yet G has uncountably many homomorphisms to Z.

preprint1994arXivOpen access
Andreas BlassRüdiger Göbel
math.LO
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Andreas BlassRüdiger Göbel

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