groups $G$ such that $Aut(G)$ is trivial
12455
$|G|>2$ implies $G$ has non trivial automorphism
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
151193
Simple subgroup of Symmetric Group
39425
Surprising but simple group theory result on conjugacy classes
61373
A normal subgroup that is not a characteristic
85018
When is the automorphism group of the Cayley graph of $G$ just $G$?
135701
An example of a group such that $G \cong G \times G$
104509
The center of $A_n$ is trivial for $n \geq 4$
151699
Group of inner automorphisms of a group $G$
48393
Abelian groups of order n.
111375
Normality of subgroups and Sylow groups under homomorphisms...
76504
Non-trivial cyclic group with unique generator
129830
A group with no proper non-trivial subgroups
2153
How to get a homomorphism from $\mathbb{Z}\to G$, for $G$ a non-trivial group?
114221
A Group $G$ is soluble $\iff G^{(k)}=\{e\}$ for some $k$
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
10602
Monotone Union of subgroups being subgroup