Consider the map $\psi : G \rightarrow Aut(G)$ given by $\psi(g) = \phi_{g}.$ Prove that $\psi$ is a homomorphism
7890
Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
121257
Image of Homomorphism of Lie groups
95806
Proving commutativity of convolution $(f \ast g)(x) = (g \ast f)(x)$
61593
Adjoint map is Lie homomorphism
50130
$\operatorname{Aut}(V)$ is isomorphic to $S_3$
111375
Normality of subgroups and Sylow groups under homomorphisms...
124140
Quick way to find the number of the group homomorphisms $\phi:{\bf Z}_3\to{\bf Z}_6$?
62711
Canonical map $R/(I\cap J)\rightarrow R/I\times _{R/(I+J)} R/J$ is an isomorphism
85768
The function $f:G \rightarrow G$ defined by $f(x)=x^2$ is a homomorphism iff G is abelian.
142851
Every group homomorphism from $(\mathbb{Q}, +)$ to $(\mathbb{Q}, \times)$ is the trivial map.
133660
When can a homomorphism be determined entirely by its generators
3462
Proving a set of automorphisms of a group is a group under composition
43759
Prove that the set $\mathrm{Aut}(G)$ of all automorphisms of the group $G$ with the operation of taking the composition is a group
108691
Characterize the natural numbers $n$ such that there is a surjective group homomorphism from $S_n$ to $S_{n-1}$.
137011
showing $\psi: R\to \mathbb C$ is ring isomorphism.
4228
Prove that the only automorphism of $\mathbb{Q}(\sqrt[3]{2})$ is the identity automorphism.
12104
How to prove this result involving the quotient maps and connectedness?