Which of the following are true?

(A). Let G = be a cyclic group of order n, then G = k> if and only if gcd(k, n) = 1

(B). Let G be a group and let a be an element of order n in G. If a^k = e, then n divides k.

(C). The centre of a group G may not be a subgroup of the group G.

(D). For each 'a' in a group G, the centralizer of 'a' is a subgroup of group G

Choose the correct answer from the options given below: