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Suppose that *G* is a group with subgroups *K* ≤ *H* ≤ *G*. Suppose that *K* is normal in *G*. Let *G* act on *G*/*H*, the set of left cosets of *H*, by left multiplication. Prove that if k ∈ *K*, then left multiplication of *G*/*H* by k is the identity permutation on *G*/*H*.

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