Let G be an abelian group, Ha subgroup of G, and n a fixed positive integer. (a) Let Hn = (aEGla" EH}. Prove that H, is a subgroup of G. (b) Show part (a) is false if G is not abelian as follows: Take G (S3, o), H = ((1)} (the identity subgroup), and n = 2 %3D Show H2 = {y E S3Iy2 (1)} is not a subgroup. %3D

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