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Abelian p-Groups A and B Such that $\operatorname{Tor}(A, G) \cong \operatorname{Tor}(B, G), G$ Reduced

Doyle Cutler
Proceedings of the American Mathematical Society
Vol. 91, No. 1 (May, 1984), pp. 12-14
DOI: 10.2307/2045259
Stable URL: http://www.jstor.org/stable/2045259
Page Count: 3
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Abelian p-Groups A and B Such that $\operatorname{Tor}(A, G) \cong \operatorname{Tor}(B, G), G$ Reduced
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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 nth Ulm invariant of C is zero if the nth Ulm invariant of A is finite. Then for all reduced abelian groups $G, \operatorname{Tor}(G, A) \cong \operatorname{Tor}(G, A \oplus C)$.

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