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Problem 26 of L. Fuchs

Author: Chin Shui Hsü
Journal: Proc. Amer. Math. Soc. 42 (1974), 81-84
MSC: Primary 20K25
MathSciNet review: 0335660
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Abstract: This solves the following problem: Which Abelian groups are the inverse limits of Abelian groups, each of which is a finite direct sum of quasi-cyclic and bounded Abelian groups? (Here quasi-cyclic means isomorphic to some $ Z({p^\infty })$.) A necessary and sufficient condition for an Abelian group to be such is that it takes the form $ {A_r} \oplus \Pi_p\operatorname{Hom}_z({A_p},Z({p^\infty }))$ where $ {A_r}$ is complete and reduced, the $ {A_p}$ are torsion-free and the direct product is taken over the set of prime numbers.

References [Enhancements On Off] (What's this?)

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  • [2] C. U. Jensen, On the vanishing of $ \mathop{\lim}\limits_ \leftarrow ^{(i)}$, J. Algebra 15 (1970), 151-166. MR 41 #5460. MR 0260839 (41:5460)
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Article copyright: © Copyright 1974 American Mathematical Society

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