Determine the number of cyclic subgroups of order 15 in $ \scriptstyle Z_{90}\oplus Z_{36} $.
I found that there were 32 elements: 8 from when |a| = 5, |b| = 3 and 8 more when |a| = 15, |b| = 1 or 3. Then, each subgroup of order 15 has 8 generators and there can be no overlap, so we have 32/8 = 4 subgroups. Example 5 on p155 is very helpful.
