I'm not sure how to begin the second part of the following problem.

For part (i) I just set up a 4x4 matrix with rows (8, 0, 0, 0), (0, 12, 0, 0) (which take into account of G) and (4, 8, 1, 0), (1, 1, 2, 3) (corresponding to H), row reduced over the integers to get a diagonal matrix with entries 1, 1, 4, 12996, so $\displaystyle H\approx \{0\}\times\{0\}\times \mathbb{Z}_4\times \mathbb{Z}_{12996} \approx \mathbb{Z}_{2^2}\times \mathbb{Z}_{2^2} \times \mathbb{Z}_{3^2} \times \mathbb{Z}_{19^2}$. Their accuracy is irrelevent to my question: I would just appreciate a hint as to how (ii) can be attacked using (i).Quote:

Originally Posted byThe problem

Many thanks for your help