inuyasha

How to prove subgroups of cyclic groups are cyclic? I searched it on the Internet and found out a common way is like this:

According to Lagrange Theorem, the vth subgroup of a pth group has v = p\t. So the subgroup is (a ^ t).

But what if the n of a nth cyclic group is infinite?

According to Lagrange Theorem, the vth subgroup of a pth group has v = p\t. So the subgroup is (a ^ t).

But what if the n of a nth cyclic group is infinite?