For $\phi$ as a homomorphism not onto show not normal subgroup
44165
the image of normal subgroups
113413
How do I show that two groups are not isomorphic?
155054
$G$ be a group and $H$ be a normal subgroup of index $p$ ( a prime ) ; suppose $K$ is a subgroup of $G$ not contained in $H$ , then $G=HK$?
144065
Proving $\phi(G)$ is cyclic if $\phi$ : $G \to H$ is group homomorphism and $G$ is cyclic
151029
The number of non normal subgroups of a group cannot be $1$?
7938
Number of Homomorphisms from $\Bbb{Z}_m$ to $\Bbb{Z}_n$
113925
Normal Subgroup Counterexample
11710
How to show that $\mathbb{Q}$ is not $G_\delta$
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
67272
Deduce that if $G$ is a finite $p$-group, the number of subgroups of $G$ that are not normal is divisible by $p$
109987
No homomorphism from $Z_{16}\oplus Z_{2}$ onto $Z_{4}\oplus Z_{4}$.
143451
Homomorphism from $(\Bbb Q,+)$ to a finite group
5906
All group homomorphism from $ \mathbb{Z} _m $ to $\mathbb{Z}_n $
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
106347
Why is the image of a homomorphism a subgroup of the codomain?
88930
Homomorphism between free groups