Question about normal subgroup that contains Kernel of a homomorphism
109236
Subgroups containing kernel of group morphism to an abelian group are normal.
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
47623
The set of all complex homomorphisms of abelian group $G$ has the same structure as $G$
84132
Number of preimages of a group element under a homomorphism.
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
119648
For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?
61334
Application of Main Homomorphism Theorem
125244
Equivalent definitions of normal subgroups
106779
How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$
40069
The image of a homomorphism is a group?
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
88199
The commutator subgroup of a quotient in terms of the commutator subgroup and the kernel
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.
15630
Normal subgroup of prime order is characteristic
642
Does a surjective ring homomorphism have to be surjective on the unit groups?
55493
Showing that the path-connected component of the identity matrix in a subgroup of $GL_n(\Bbb R)$ is a normal subgroup
88930
Homomorphism between free groups