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Determine the number of cyclic subgroups of order 15 in <math>\scriptstyle Z_{90}\oplus Z_{36}</math>. | Determine the number of cyclic subgroups of order 15 in <math>\scriptstyle Z_{90}\oplus Z_{36}</math>. | ||
| − | I found that there were 32 | + | 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. |
Latest revision as of 20:44, 8 October 2008
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.
