For a group homomorphism, does there exist a subgroup of the domain isomorphic to the image?
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
150961
An example for a homomorphism that is not an automorphism
84869
Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
104505
Is every normal subgroup the kernel of some endomorphism?
35353
Isomorphic quotient groups $\frac{G}{H} \cong \frac{G}{K}$ imply $H \cong K$?
27728
Question on a homomorphism of a set G.
33294
The correspondence theorem for groups
111375
Normality of subgroups and Sylow groups under homomorphisms...
153797
Is a quotient group a subgroup?
35961
In what sense of "structure" do group homomorphisms "preserve structure"?
90010
Can we ascertain that there exists an epimorphism $G\rightarrow H$?
133627
If $\phi(g)=g^3$ is a homomorphism and $3 \nmid |G|$, $G$ is abelian.
157145
Subgroup of $S_8$ isomorphic to $G$
128443
Isomorphism between finite groups
106347
Why is the image of a homomorphism a subgroup of the codomain?
134858
Abelian Group Homomorphism
30236
isomorphic groups related in direct product.