A surjective homomorphism and normal subgroups
1220
Have $\alpha:G \to H$. If a subgroup $U$ is normal in $H$ prove the pre-image of $U$ is normal in $G$.
1026
Ring homomorphism with $\phi(1_R) \neq1_S$
62454
Let $f : G → G_1$ be a surjective homomorphism (also called epimorphism) from $G$ to another group $G_1$. Prove that $f(Z(G)) \subseteq Z(G_1)$.
142413
Normal Subgroups of $SU(n)$
83710
Order of a homomorphism of groups
34234
Kernel of injective group homomorphism
134858
Abelian Group Homomorphism
109236
Subgroups containing kernel of group morphism to an abelian group are normal.
121244
Homomorphisms and automorphisms on polynomial rings
26661
Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
84132
Number of preimages of a group element under a homomorphism.
97928
Normal subgroup of a normal subgroup
45576
A surjective homomorphism between finite free modules of the same rank
88930
Homomorphism between free groups
126644
Simple module and homomorphisms
18343
Counting homomorphisms between $\Bbb Z$ and $\Bbb Z_n$ and also between $\Bbb Z_n$ and $\Bbb Q$
125244
Equivalent definitions of normal subgroups