The equivalence of ×^{𝑡}𝐶≈×^{𝑡}𝐷 and 𝐽×𝐶≈𝐽×𝐷

Hirshon, Ronald

doi:10.1090/S0002-9947-1979-0525676-3

The equivalence of $\times ^{t}C\approx \times ^{t}D$ and $J\times C\approx J\times D$
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Trans. Amer. Math. Soc. 249 (1979), 331-340 Request permission

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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