Problem with showing that group is isomorphic, cyclic and its subgroup is normal
104460
When a group is cyclic
135710
Cyclic Automorphism group
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
34902
If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every subgoup of $H$ is normal in $G$.
28108
Proving the kernel is a normal subgroup.
44165
the image of normal subgroups
158074
Cyclic group $G$ with generator $ab$.
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
125498
Check whether subgroup is normal in $ S_4$
63780
to show characteristic subgroup is normal in G
113413
How do I show that two groups are not isomorphic?
54911
The preimage of a normal subgroup under a group homomorphism is normal
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
113013
Let $M$ and $N$ be two normal subgroups of $G$. Show that $M \cap N$ is also normal in $G$. Then show that $G/(M \cap N) \cong (G/M) \times (G/N)$
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
155219
Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.
90437
Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.