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For questions about groups whose elements commute.

0 votes

Abelian group of finite rank

Yes, i think it is true. Take $A\otimes_{\mathbb{Z}}\mathbf{Z}_p$ (tensor product with $p$-adic ring). If $e_1, ..., e_n\in A$ is basis of $A/pA$, then $A\otimes_{\mathbb{Z}}\mathbf{Z}_p = e_1\otimes_ …
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