New posts in Cyclic Groups

For what $n$ is $U_n$ cyclic?

A subgroup of a cyclic group is cyclic - Understanding Proof

Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .

If $|G|>1$ is not prime, there exists a subgroup of $G$ which is not $G$ or $e$.

Order of automorphism group of cyclic group

Give an example of a noncyclic Abelian group all of whose proper subgroups are cyclic.

Homomorphism between cyclic groups

If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every subgoup of $H$ is normal in $G$.

If $G/Z(G)$ is cyclic, then $G$ is abelian

Explanation why an abelian tower admits a cyclic refinement