Please Login to access more options.
Problem 65 (Subgroups Of Cyclic Groups Are Cyclic)
Suppose that $G$ is a cyclic group generated by $a$. Suppose that $H$ is a subgroup of $G$. Prove that there exists $k\in\mathbb{Z}$ such that $H = \left<a^k\right>$. In other words, prove that $H$ is itself a cyclic group.
Click to see a hint.
How can you get the smallest positive integer $k$ such that $a^k\in H$?
The following pages link to this page.