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Feb 13 at 16:33 comment added Daniel Yes. I assume $|G|=|G'|<\infty$, but I actually find the question interesting even without this condition.
Feb 9 at 15:20 history edited YCor
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Feb 9 at 15:20 comment added YCor Are the groups assumed to be finite?
Feb 9 at 14:26 history asked Daniel CC BY-SA 4.0