Let\(G\)beafinitegroupand\(H<G\).If\([G:H]=2\),then\(gH=Hg\).Proof:If\([G:H]=2\),thenthereareonlytwocosetsof\(H\)in\(G\),andoneofthecosetsis\(H\)itself,i.e.,\[G=H\cupgH=H\cupHg,\]where\(H\cap