Show that every proper subgroup of $S_3$ is cyclic.
90453
How can I find cyclic subgroups of $S_3$?
117899
At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic
32620
Is every group of order $21$ cyclic?
158074
Cyclic group $G$ with generator $ab$.
85677
Is there a free subgroup of rank 3 in $SO_3$?
123711
Cyclic group with exactly 3 subgroups: itself $\{e\}$ and one of order $7$. Isn't this impossible?
92430
Show that the group is cyclic.
14890
Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
152662
Proving that any finite cyclic group of order $n$ is isomorphic to $$
152589
How to show that if $G$ is union of three proper subgroups, then there is an epimorphism from $G$ to the Klein 4-group?
13764
Homomorphisms from $\mathbb{Z} \rightarrow S_3$.
98145
If $G$ is cyclic then $G/H$ is cyclic?
41709
Show that the symmetric group $S_p = $, where $\sigma$ is any transposition and $\tau$ is any p- cycle and p is a prime number.
61394
The product of finitely many cyclic groups is cyclic
73402
Showing that $(\mathbb{Z}/p^{a}\mathbb{Z})^*$ is a cyclic group
23394
If $G/Z(G)$ is cyclic, then $G$ is abelian
61513
Prove that all cyclic groups of the same order are isomorphic