Let G be a group and let Z(G) be the centre of G. (i) What is an alternative way of saying Z(G) = G? (ii) Give an example of a group G such that |G| = 6 and Z(G) + {e}. Give an example of a group G such that |G| = 6 and Z(G) = {e}. (No proofs are required.) (iii) Does there exist a group G such that |G| > 2 but |Z(G)| = 2? Give an example, or %3D prove that such a group does not exist.

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A: We have: to use definition of homomorphism:

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