$f \colon G_1 \to G_2$ group homomorphism, then $G_1 / N_1 \cong G_2 / N_2$
115663
Proving an isomorphism using the isomorphism theorems
83710
Order of a homomorphism of groups
110390
Order of group $GL_{2}\left( \mathbb{F}_{p}\right) $
140471
Is $ G \cong G/N \times N$?
4838
For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian
45727
If $G$ contains a normal subgroup $H \cong \mathbb{Z_2}$ such that $G/H$ is infinite cyclic, then $G \cong \mathbb{Z} \times \mathbb{Z_2}$
55900
Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
40383
Is it true that $|g| = |\phi(g)|$ for all homomorphisms $\phi: G \to G$ and $g \in G$?
134858
Abelian Group Homomorphism
89415
Number of homomorphisms from $(\mathbb Q^+ , \,\cdot\,)$ to $(\mathbb Z_n , +)$
85768
The function $f:G \rightarrow G$ defined by $f(x)=x^2$ is a homomorphism iff G is abelian.
85129
If $H_1, H_2\leq G$ are such that $H_1\cong H_2$ then $G/H_1\cong G/H_2$?
40069
The image of a homomorphism is a group?
125582
Let $\phi:G_1\to G_2$ be a group homomorphism. Show $\phi(g^{-1})=(\phi(g))^{-1}$.
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
121257
Image of Homomorphism of Lie groups
95299
What can you say about $f$ and $g$ in the case that $fg$ is 1) Injective, 2) Surjective - Cohn - Classic Algebra Page 15