$Aut(G)$ is abelian if and only if $G$ is cyclic.
106123
Is there a finite abelian group $G$ such that $\textrm{Aut}(G)$ is abelian but $G$ is not cyclic?
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
13631
Showing group with $p^2$ elements is Abelian
11003
Proving that $G/N$ is an abelian group
84
For what $n$ is $U_n$ cyclic?
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
106809
$f: G→G$ defined by $f(x) =x^2$ is a homomorphism if and only if $G$ is abelian.
74964
Showing Galois Group is Abelian
147517
Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
26624
Prove that is group is abelian
66510
A group is abelian if and only if the center of the group is all the group
144258
How to show a group is cyclic?
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
97565
Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
14528
Proof that all abelian simple groups are cyclic groups of prime order
49768
If Gal(K,Q) is abelian then |Gal(K,Q)|=n