Prove that if Aut($G$) is the trivial group, then so is $G$?
12455
$|G|>2$ implies $G$ has non trivial automorphism
151699
Group of inner automorphisms of a group $G$
46904
Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
79452
How to prove that it is a group?
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
121034
Follow-up to question: Aut(G) for G = Klein 4-group is isomorphic to $S_3$
135039
${\rm Aut}(G)$ is cyclic $\implies G$ is abelian
99346
Prove a result on transitive group actions.
29717
Not sure how to go about this group theory proof
74586
Prove that every group of order $4$ is abelian
116707
Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.
42891
Prove that $Z(G)$ which is the center of $G$ is a subgroup of $G$
158490
Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
107511
If $G$ and $H$ are nonisomorphic group with same order then can we say that $Aut(G)$ is not isomorphic to $Aut(H)$?
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
26624
Prove that is group is abelian