Particular nontrivial group has a nonidentity automorphism
12455
$|G|>2$ implies $G$ has non trivial automorphism
44258
Conditions under which group solvability is invariant under an homomorphism.
40321
$\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.
134858
Abelian Group Homomorphism
133664
When the automorphism group is trivial......
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
69820
A nontrivial p-group has nontrivial center
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
7640
Exactly one nontrivial proper subgroup
33294
The correspondence theorem for groups
128692
Example of an infinite group where every element except identity has order 2
76504
Non-trivial cyclic group with unique generator
73988
Characterize the groups $G$ for which the map $\iota: G \to G$, sending $x \mapsto x^{-1}$ for all $x \in G$, is an automorphism of $G$
150207
Non isomorphic subgroups of cyclic groups
114320
Showing that if the center of a group is trivial, then the center of its automorphism group is trivial
62277
Cayley tables for two non-isomorphic groups of order 4.