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a) Let H be a subgroup of a group G satisfying [G ∶ H] = 2....

a) Let H be a subgroup of a group G satisfying [G ∶ H] = 2. If there are elements a, b ∈ G such that ab ∈/ H, then prove that either a ∈ H or b ∈ H. (b) List the left and right cosets of H = {(1), (23)} in S3. Are they the same collection?

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