Number of homomorphisms $f:S_3 \to S_3$ when $\ker(f)=(1)$.
72853
What is the number of automorphisms (including identity) for permutation group $S_3$ on 3 letters?
1026
Ring homomorphism with $\phi(1_R) \neq1_S$
83710
Order of a homomorphism of groups
133627
If $\phi(g)=g^3$ is a homomorphism and $3 \nmid |G|$, $G$ is abelian.
32428
Group homomorphisms and which of the following statements are true (NBHM-$2014$)
33455
Question on group homomorphisms involving the standard Z-basis
64025
Ring homomorphisms from $\Bbb Q$ into a ring
32443
Find the kernel of a ring homomorphism $f(x)\to f(\sqrt 2)$
130081
Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
28252
How many homomorphisms are there from $\Bbb Z_{20}$ onto $\Bbb Z_{8}$? How many are there to $\Bbb Z_{8}$?
26110
Canonical isomorphism between $\mathfrak{so}(3)$ and $\mathbb R^3$ with vector cross product
158282
Finite order of an element $f(g)$ of a homomorphism $f$
149029
3-manifold examples of homomorphisms between fundamental groups that are not induced by continuous maps
140557
Counting ring homomorphisms from $\mathbb{Z}[x,y]/(x^3+y^2-1)$ to $\mathbb{Z_7}$
106550
The bijection between homogeneous prime ideals of $S_f$ and prime ideals of $(S_f)_0$
57732
Rings of fractions and homomorphisms