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Oct 13, 2018 at 8:18 comment added YCor Note: the simple computation shows, in an arbitrary group $G$ with subgroup $H$, if $A,B$ are left-or-right cosets of $H$ and $[A,B]=1$, then $H$ is abelian and $A,B$ are both included in the centralizer of $H$.
Oct 12, 2018 at 15:43 history edited YCor CC BY-SA 4.0
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Oct 12, 2018 at 15:43 vote accept Denis Serre
Oct 12, 2018 at 9:23 history answered YCor CC BY-SA 4.0