一个局部紧的不可分阿贝尔群，其character群是无挠的且可分
A locally compact non divisible abelian group whose character group is torsion free and divisible
摘要：
Halmos在《关于实数线的评论》（Bull. Amer. Math. Soc.，50（1944），877-878]证明了如果G是Hausdorff局部紧拓扑阿贝尔群，且G的特征标群是无挠的，则G是可分的。我们证明这种说法是错误的，通过提出一个家庭的反例。而其他反例是已知的（见[D]）。L. Armacost，The structure of local紧阿贝尔群，1981]），我们还提出了一族更强的反例，证明了即使假设G的特征标群是无无挠的且可除的，也不能得出G是可除的。
英文摘要：
It has been claimed by Halmos in [Comment on the real line, Bull. Amer. Math. Soc., 50 (1944), 877-878] that if G is a Hausdorff locally compact topological abelian group and if the character group of G is torsion free then G is divisible. We prove that such claim is false, by presenting a family of counterexamples. While other counterexamples are known (see [D. L. Armacost, The structure of locally compact abelian groups, 1981]), we also present a family of stronger counterexamples, showing that even if one assumes that the character group of G is both torsion free and divisible, it does not follow that G is divisible.
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