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Maximal normal subgroups

Find all maximal normal subgroups of Z[p] × Z[q], where p and q are relatively prime.

Would the elements from Z[p] have to be one that are relatively prime to q and vice versa?

Solution Preview

First, Z[p]xZ[q] is an abelian group, so each subgroup is normal.
Second, each subgroup of Z[p]xZ[q] has the form GxH, where G is a
subgroup of Z[p] and H is a ...

Solution Summary

This is a question regarding maximal normal subgroups.