When the automorphism group is trivial......
12455
$|G|>2$ implies $G$ has non trivial automorphism
126771
Group element not taken to its inverse by any automorphism
13761
Automorphisms in $\mathbb{Z}_n$
126790
Basic Isomorphism Question
114811
Characteristic subgroups and automorphisms
40069
The image of a homomorphism is a group?
111168
Automorphisms of a finite non-abelian group
46263
Automorphisms of infinite abelian groups
32428
Group homomorphisms and which of the following statements are true (NBHM-$2014$)
83710
Order of a homomorphism of groups
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 $G$
23941
Normal Subgroups that Intersect Trivially
66464
Faithful group actions for singleton group or for empty set
90256
Example of a simple graph isomorphic to a permutation group.
66806
A nonsplit short exact sequence of abelian groups with $B \cong A \oplus C$
6385
Minimal counterexamples of the isomorphism problem for integral group rings
44258
Conditions under which group solvability is invariant under an homomorphism.