Question: (a) Prove Theorem 16.4. (b) Extending the idea developed in Theorem 16.4 and Example 16.9 to the group Z6 Z6 Z6 = Z36

(a) Prove Theorem 16.4.
(b) Extending the idea developed in Theorem 16.4 and Example 16.9 to the group Z6 × Z6 × Z6 = Z36 answer the following.
(i) What is the order of this group?
(ii) Find a subgroup of Z36 of order 6, one of order 12, and one of order 36.
(iii) Determine the inverse of each of the elements (2, 3, 4), (4, 0, 2), (5, 1, 2).

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