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Abelian $ p$-groups $ A$ and $ B$ such that $ {\rm Tor}(A,\,G)\cong {\rm Tor}(B,\,G),$ $ G$ reduced


Author: Doyle Cutler
Journal: Proc. Amer. Math. Soc. 91 (1984), 12-14
MSC: Primary 20K40; Secondary 20K10
DOI: https://doi.org/10.1090/S0002-9939-1984-0735554-X
MathSciNet review: 735554
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Abstract: Let $ A$ be an abelian $ p$-group having all of its finite Ulm invariants nonzero. Let $ C$ be a countable direct sum of cyclic $ p$-groups such that for each nonnegative integer $ n$, the $ n$th Ulm invariant of $ C$ is zero if the $ n$th Ulm invariant of $ A$ is finite. Then for all reduced abelian groups $ G$, $ {\operatorname{Tor}}(G,A) \cong {\text{Tor}}(G,A \oplus C)$.


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

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  • [2] D. Cutler, Torsion products of abelian $ p$-groups, J. Algebra 77 (1982), 158-161. MR 665170 (83h:20058)
  • [3] L. Fuchs, Infinite abelian groups, Vols. 1 and 2, Academic Press, New York, 1970 and 1973.
  • [4] R. J. Nunke, On the structure of Tor. II, Pacific J. Math. 22 (1967), 453-464. MR 0214659 (35:5508)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0735554-X
Keywords: Abelian $ p$-group, torsion product
Article copyright: © Copyright 1984 American Mathematical Society

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