A hard question on surjective group homomorphism
90010
Can we ascertain that there exists an epimorphism $G\rightarrow H$?
44258
Conditions under which group solvability is invariant under an homomorphism.
47623
The set of all complex homomorphisms of abelian group $G$ has the same structure as $G$
90616
When is mapping $g$ to $g^{-1}$ a group homomorphism?
5906
All group homomorphism from $ \mathbb{Z} _m $ to $\mathbb{Z}_n $
100149
If there are injective homomorphisms between two groups in both directions, are they isomorphic?
40993
Let $f:G\to G'$ be a surjective homomorphism. Prove that if $G$ is cyclic, then $G'$ is cyclic.
108691
Characterize the natural numbers $n$ such that there is a surjective group homomorphism from $S_n$ to $S_{n-1}$.
111049
Groups with given automorphism groups
6466
Image of subgroup and Kernel of homomorphism form subgroups
121257
Image of Homomorphism of Lie groups
34234
Kernel of injective group homomorphism
134858
Abelian Group Homomorphism
129858
"Almost" ring homomorphism
6023
Surjectivity of Composition of Surjective Functions
111375
Normality of subgroups and Sylow groups under homomorphisms...
62454
Let $f : G → G_1$ be a surjective homomorphism (also called epimorphism) from $G$ to another group $G_1$. Prove that $f(Z(G)) \subseteq Z(G_1)$.