- #36
Infrared
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I think we went overkill on detail. For the purpose of the problem, you could probably just say: labeling the vertices associates to each element of [itex]D_{2n}[/itex] a permutation in [itex]S_n[/itex]. This association is a homomorphism because multiplication in [itex]D_{2n}[/itex] corresponds to composing permutations. This association is injective because only the identity element of [itex]D_{2n}[/itex] fixes all vertices. Then write down the map explicitly as we did.