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Find the left cosets and the right cosets of the subgroup H of G. Is it...

Find the left cosets and the right cosets of the subgroup H of G. Is it the case that aH = Ha for all a ∈ G? Also find (G : H).

a) H = {ι, (1 2)(3 4), (1 3)(2 4), (1 4)(2 3)}, G = A4

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