(New page: Determine the number of cyclic subgroups of order 15 in <math>\scriptstyle Z_90\oplus Z_36</math>) |
|||
| (4 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | Determine the number of cyclic subgroups of order 15 in <math>\scriptstyle | + | Determine the number of cyclic subgroups of order 15 in <math>\scriptstyle Z_{90}\oplus Z_{36}</math>. |
| + | |||
| + | 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 19:44, 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.
