Infinite rank Butler groups

Authors:
Manfred Dugas and K. M. Rangaswamy

Journal:
Trans. Amer. Math. Soc. **305** (1988), 129-142

MSC:
Primary 20K20; Secondary 20K35, 20K40

DOI:
https://doi.org/10.1090/S0002-9947-1988-0920150-X

MathSciNet review:
920150

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Abstract: A torsion-free abelian group is said to be a Butler group if for all torsion groups . It is shown that Butler groups of finite rank satisfy what we call the torsion extension property (T.E.P.). A crucial result is that a countable Butler group satisfies the T.E.P. over a pure subgroup if and only if is decent in in the sense of Albrecht and Hill. A subclass of the Butler groups are the so-called -groups. An important question left open by Arnold, Bican, Salce, and others is whether every Butler group is a -group. We show under that this is indeed the case for Butler groups of rank . On the other hand it is shown that, under ZFC, it is undecidable whether a group for which for all countable torsion groups is indeed a -group.

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DOI:
https://doi.org/10.1090/S0002-9947-1988-0920150-X

Keywords:
Torsion-free abelian groups,
Butler groups,
pure subgroups

Article copyright:
© Copyright 1988
American Mathematical Society