Suppose G is a group with |G| > 1. Which of the following are true? (i): C = {g € G | ga = ag for any a € G} is a normal subgroup of G. (ii): If K is a normal subgrup of G, then there is a homomorphism G → G/K has kernel K. (iii): If K is a normal subgroup of G such that G/KG, then K = G. (iv): G must contain a non-trivial proper normal subgroup. ***

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A: " Let G be a group and H ≤ G.The subgroup H is normal in its normalizer NG(H), this imply that NG(H)…

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A: be the set of elements  of  such that  that is the We have to show that  is a subgroup of

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