Existence of nontrivial automorphism for a group $G$ with $o(G)>2$
12455
$|G|>2$ implies $G$ has non trivial automorphism
139451
Prove that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection
135710
Cyclic Automorphism group
85018
When is the automorphism group of the Cayley graph of $G$ just $G$?
111375
Normality of subgroups and Sylow groups under homomorphisms...
44258
Conditions under which group solvability is invariant under an homomorphism.
150207
Non isomorphic subgroups of cyclic groups
2153
How to get a homomorphism from $\mathbb{Z}\to G$, for $G$ a non-trivial group?
41688
An elementary problem in Group Theory: the unique noncyclic group of order 4
46904
Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
9612
Frattini subgroup $Φ ( G )$ is not trivial
61550
Existence of elements of order $p^k$ in a finite group
44361
An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity
101079
Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
119648
For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?
71035
Non abelian subgroup of a abelian group.
46263
Automorphisms of infinite abelian groups