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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The equivalence of $ \times \sp{t}C\approx \times \sp{t}D$ and $ J\times C\approx J\times D$


Author: Ronald Hirshon
Journal: Trans. Amer. Math. Soc. 249 (1979), 331-340
MSC: Primary 20F99
MathSciNet review: 525676
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Abstract: Let C satisfy the maximal condition for normal subgroups and let $ \times {\,^t}C\, \approx \, \times {\,^t}D$ for some positive integer t. Then $ C\, \times \,J\, \approx \,D\, \times \,J$ where J is the infinite cyclic group. If $ \times {\,^s}C\, \approx \, \times {\,^t}D$ and $ s \geqslant \,t$, there exists a finitely generated free abelian group S such that C is a direct factor of $ D\, \times \,S$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0525676-3
PII: S 0002-9947(1979)0525676-3
Keywords: J replacement, cancelation
Article copyright: © Copyright 1979 American Mathematical Society