# Math Help - direct sume noncyclic subgroup

1. ## direct sume noncyclic subgroup

List four elements of Z20+Z5+Z60that form a noncyclic subgroup. First, what would a noncyclic subgroup in this look like, I am not sure

2. Originally Posted by wutang
List four elements of Z20+Z5+Z60that form a noncyclic subgroup. First, what would a noncyclic subgroup in this look like, I am not sure
Is this $\mathbb{Z}_{20}\oplus\mathbb{Z}_5\oplus\mathbb{Z}_ {60}$?

3. That is right.

4. would (0,0,0), (10,0,30), (0,0,30), and (10,0,0) work as a noncyclic subgroup?

5. Originally Posted by wutang
would (0,0,0), (10,0,30), (0,0,30), and (10,0,0) work as a noncyclic subgroup?
yes

6. thanks again, fancymouse you are a lifesaver!