Question: let G be a group and H be a subgroup of G. Define the index of h in g to b the number of left

let G be a group and H be a subgroup of G. Define the index of h in g to b the number of left cosets of H in G. we will denote the index by [G : H].

let G be a group and H be a subgroup of G. Define
Suppose that [G : H) = 2. If a and b are not in H, show that ab E H

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