Suppose that $\mathbb Z_p \times A \simeq \mathbb Z_p \times B$, where $p$ is prime. Is it true, that $A \simeq B$?
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$\begingroup$ If $A,B$ are abelian, the answer is yes. See Gone's answer here: math.stackexchange.com/questions/2193/… $\endgroup$– user27126Apr 18, 2013 at 3:09
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$\begingroup$ Thank you, it is very interesting. But it is not use, that $p$ is prime. $\endgroup$– Alex-omskApr 18, 2013 at 3:34
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$\begingroup$ @Alex-mosk, so is there any restriction about $A,B$ at all? It would be good to know the context of your question. $\endgroup$– user27126Apr 18, 2013 at 3:43
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$\begingroup$ This is true with no assumptions on $A, B$. See the link. $\endgroup$– Qiaochu YuanApr 18, 2013 at 3:56
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