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6. Let G = S5 the group of bijective maps on Ω5 = {1,2,3,4,5}. Let H...

6. Let G = S5 the group of bijective maps on Ω5 = {1,2,3,4,5}. Let H = {σ ∈ G : σ(5) = 5}.Let K be a subgroup of G. Prove that KH = G if and only if 5 divides |K|.

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