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let's suppose I have two subgroups [itex]R[/itex] and [itex]T[/itex], and I know that in general they do not commute: that is, [itex]rt\neq tr[/itex] for some [itex]r\in R[/itex], [itex]t\in T[/itex].

Is it possible, perhaps after making specific assumptions on R and T, to find some [itex]r'\in R[/itex], and [itex]t'\in T[/itex] such that: [tex]rt=t'r'[/tex].

This is possible, for example, with some matrix manipulations if R and T are respectively the groups of rotations and translations in 2D. I was wondering if it is possible to find a more general algebraic approach without making explicit how R and T are defined.

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# Commutation between subgroups

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