If there exists an epimorphism from a group $G_1$ to $G_2$ that is not one-to-one, then can $G_1$ and $G_2$ be isomorphic?
27436
Does $G\cong G/H$ imply that $H$ is trivial?
98731
Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
33702
Is this an isomorphism possible?
30178
Homeomorphism $(\mathbb{CP}^1)^m/S_m \overset{\sim}{\to} \mathbb{CP}^m$?
25728
A second isomorphism theorem for action on cosets
37351
Group of Order $p^2$ Isomorphic to $\mathbb{Z}_{p^2}$ or $\mathbb{Z}_{p}$ $\times$ $\mathbb{Z}_{p}$
158892
Surjective endomorphism of abelian group is isomorphism
154318
Can a field be isomorphic to its subfield?
52556
Isomorphism of $S^1$.
59902
Example of $2$ non-isomorphic groups that have the same quotients
118354
Epimorphism and Monomorphism = Isomorphism?
121449
An isomorphism from $GL_{2}(\mathbb{F_{2}})$ to $S_{3}$
121034
Follow-up to question: Aut(G) for G = Klein 4-group is isomorphic to $S_3$
108044
Isomorphic extensions of $\mathbb Z_3$ by $\mathbb Z_3 \times \mathbb Z_3$ which are not equivalent
113413
How do I show that two groups are not isomorphic?
28210
A finite group with exactly $2$ conjugacy classes isomorphic to $\mathbb{Z}_2$
18540
Isomorphism from $\mathbb{C}[G]$ to $\prod_{i=1}^h M_{n_i}(\mathbb{C})$.