question about cyclic groups and quotient groups
2304
What is the quotient of a cyclic group of order $n$ by a cyclic subgroup of order $m$?
73402
Showing that $(\mathbb{Z}/p^{a}\mathbb{Z})^*$ is a cyclic group
41688
An elementary problem in Group Theory: the unique noncyclic group of order 4
135710
Cyclic Automorphism group
8623
Finite subgroups of the multiplicative group of a field are cyclic
28913
How to find a generator of a cyclic group?
137949
If the quotient group $G/N$ be isomorphic to $G_2$, is $G$ isomorphic to $G_1\times G_2$ where $N$ is isomorphic to $G_1$?
141890
$G$ is a Group of order $pq$, if $G$ has exactly one subgroup of order $p$ and another with order $q$, then $G$ is cyclic ($p,q$ are prime)
151619
A finite abelian group containing a non-trivial subgroup which lies in every non-trivial subgroup is cyclic
144258
How to show a group is cyclic?
5024
Why do we define quotient groups for normal subgroups only?
31380
Exponent and abelian groups
45727
If $G$ contains a normal subgroup $H \cong \mathbb{Z_2}$ such that $G/H$ is infinite cyclic, then $G \cong \mathbb{Z} \times \mathbb{Z_2}$
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
89382
In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.
53207
Let $p$ be a prime. If a group has more than $p − 1$ elements of order $p$, why can’t the group be cyclic?
155219
Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.