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Oct 22, 2015 at 20:39 vote accept Amin
Oct 22, 2015 at 20:16 comment added Amin Thank you very much. I think a similar argument shows that the converse is also true, i.e. $H \cap K = 1$ for some $g \in G$ iff $r \ne 2s$.
Oct 22, 2015 at 17:00 history answered Derek Holt CC BY-SA 3.0