Let $G$ be a group. Suppose that $G\simeq G\times G\times G$ (here $\simeq$ is an isomorphism of groups). Is it true that in this case $G\simeq G\times G$? Of course, this question is slightly artifitial. But it is interesting whether someone knows the answer.
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3$\begingroup$ The answer is "no", see mathoverflow.net/questions/10128/when-is-a-isomorphic-to-a3 $\endgroup$– user6976Commented Apr 14, 2018 at 9:45
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