Show that if $G$ is a finite group and ${\rm Aut}(G)$ is cyclic, then $G$ is abelian.
135039
${\rm Aut}(G)$ is cyclic $\implies G$ is abelian
125559
In a group $G$, if for all $a,b,c\in G$, $ab=ca\Rightarrow b=c$, then $G$ is abelian
25235
Finite abelian groups - direct sum of cyclic subgroup
57809
For which $n$, $G$ is abelian?
117206
$|G|$ and $|{\rm Aut}(G)|$ are relatively prime $\Rightarrow$ $G$ should be cyclic?
36887
Suppose $G$ is a group of order 4. Show either $G$ is cyclic or $x^2=e$.
13355
Product of elements of a finite abelian group
106123
Is there a finite abelian group $G$ such that $\textrm{Aut}(G)$ is abelian but $G$ is not cyclic?
17077
Prove or disprove: If $H$ and $G/H$ are cyclic, then $G$ is cyclic.
58014
Prove or disprove: The automorphism group of a finite cyclic group must be cyclic.
84823
When is the group of units in $\mathbb{Z}_n$ cyclic?
129485
A subgroup of a cyclic group is cyclic - Understanding Proof
32735
If $ \langle G, \star \rangle $ is an abelian group, then for all $a, b \in G$, show that $(a \star b)^{n} = a^{n} \star b^{n}$.
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
147574
Prove of a finite cyclic group of order $n$ is isomorphic tto $(\mathbb Z_n,+)$.
1364
Let $G$ be a group in which $a^2=e$ for all elements of $a$ of $G$. Show that $G$ is Abelian.
14528
Proof that all abelian simple groups are cyclic groups of prime order