Showing a isomorphism exists between a quotient group and another group
125960
Factor groups of matrices
82559
Showing two ring homomorphisms that agree on the integers must agree on the rationals
114320
Showing that if the center of a group is trivial, then the center of its automorphism group is trivial
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
54911
The preimage of a normal subgroup under a group homomorphism is normal
150854
Identifying a quotient group (NBHM-$2014$)
157915
Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$
3462
Proving a set of automorphisms of a group is a group under composition
98474
Show the existence of a certain subgroup of F2
3907
Abelian quotient group
159005
Finding all homomorphisms between two groups - couple of questions
97565
Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
90192
Kernel and Image of a group homomorphism
38687
Isomorphism of a product $C_n \times C_m$ of cyclic groups with the cyclic group $C_{mn}$
24181
Showing that $G$ is a group under an alternative operation.
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
59902
Example of $2$ non-isomorphic groups that have the same quotients