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.
@article{bwmeta1.element.bwnjournal-article-fmv149i1p19bwm,
author = {Andreas Blass and R\"udiger G\"obel},
title = {Subgroups of the Baer--Specker group with few endomorphisms but large dual},
journal = {Fundamenta Mathematicae},
volume = {149},
year = {1996},
pages = {19-29},
zbl = {0851.20052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv149i1p19bwm}
}
Blass, Andreas; Göbel, Rüdiger. Subgroups of the Baer–Specker group with few endomorphisms but large dual. Fundamenta Mathematicae, Tome 149 (1996) pp. 19-29. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv149i1p19bwm/
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