Show that there exists a non-trivial automorphism on $G$.
12455
$|G|>2$ implies $G$ has non trivial automorphism
3462
Proving a set of automorphisms of a group is a group under composition
135701
An example of a group such that $G \cong G \times G$
63836
Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective
67383
Prove that $G'$ is not planar.
126930
Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$
151559
Please help: How to show that Aut(G) is a subgroup of Sym(G)
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
92493
If $G$ is non-abelian, then $Inn(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
7890
Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
135710
Cyclic Automorphism group
24181
Showing that $G$ is a group under an alternative operation.
119648
For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?
150961
An example for a homomorphism that is not an automorphism
102622
K is a subgroup of G. Show that K is not a normal subgroup
27728
Question on a homomorphism of a set G.